Finite Group Databasebeta

← C3×#78839 #11867048

Subgroups — C3×#78839 #11867048

Order 1152.

1079 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5828C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic, complemented
3C22×C3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
4C3×#5524C211yesmaximal, characteristic, complemented
5C32×#416C211yesmaximal, characteristic, complemented
6C3×#5113C211yesmaximal, characteristic, complemented
7C3×#4998C211yesmaximal, characteristic, complemented
8C3×#4816C212yesmaximal, complemented
9C3×#4812C212yesmaximal, complemented
10C3×#4782C212yesmaximal, complemented
11C3×#4780C212yesmaximal, complemented
12C3×#3054—31nomaximal
13#78839C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×C32×C8C2211yescharacteristic
18C32×#117C2211yescharacteristic
19C3×#950—24no—
20C3×#946C2212yes—
21C2×C3×#216C2211yescharacteristic, complemented
22C2×C3×#215C2211yescharacteristic, complemented
23C3×#938C2212yes—
24C3×#937—21no—
25C3×#935—21no—
26C2×C3×#214C2211yescharacteristic, complemented
27C2×C3×#213C2211yescharacteristic, complemented
28C3×C4×#67—22no—
29C3×#926C2211yescharacteristic
30C22×C3×C3⋊C8C2211yescharacteristic
31C2×C3×ΓL(1,𝔽25)—24no—
32C2×C3×ΓL(1,𝔽25)C2212yes—
33C2×C3×ΓL(1,𝔽25)C2212yes—
34C3×#897C2212yes—
35C3×#895C2212yes—
36C3×#886—21no—
37C3×#882—21no—
38C3×C4×D12—22no—
39C32×#103C2212yescomplemented
40C32×#102C2212yescomplemented
41C3×#821C2212yescomplemented
42C3×#816C2212yescomplemented
43C3×#808C2212yescomplemented
44C3×#807C2212yescomplemented
45C2×C3×#135—31no—
46C22×C3×M16—31no—
47C3×#525—31no—
48C3×#525—31no—
49#5828C2×C311yescharacteristic, complemented
50C2×#950C2×C311yescharacteristic, complemented
51C22×ΓL(1,𝔽25)C2×C311yescharacteristic, complemented
52#5524C2×C311yescharacteristic, complemented
53C3×#470—32no—
54C3×#469—32no—
55C3×#468—32no—
56C3×#468—32no—
57C3×#427—31no—
58C3×#416—21no—
59C3×#416—31no—
60C3×#416D311yescharacteristic, complemented
61C3×#416C2×C311yescharacteristic, complemented
62#5113C2×C311yescharacteristic, complemented
63#4998C2×C311yescharacteristic, complemented
64#4816C2×C312yescomplemented
65#4812C2×C312yescomplemented
66#4782C2×C312yescomplemented
67#4780C2×C312yescomplemented
68C23×C3×D3D411yescharacteristic
69C32×#41—22no—
70C32×#41—22no—
71C2×C32×Q8C2311yescharacteristic
72C2×C32×D4—21no—
73C2×C32×D4C2311yescharacteristic
74C22×C32×C4—21no—
75C22×C32×C4C2311yescharacteristic
76C2×C3×#67—21no—
77C2×C3×#67—22no—
78C22×C3×Dic3D411yescharacteristic
79C3×#235—22no—
80C3×#235—22no—
81C2×C3×D12—22no—
82C2×C3×D12C2311yescharacteristic
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3—22no—
85C2×C3×C4×D3—21no—
86C2×C3×C4×D3D412yes—
87C2×C3×C4×D3C2312yes—
88C2×C3×Dic6C2311yescharacteristic
89C2×C32×C8—22no—
90C2×C32×C8C2312yes—
91C32×C4⋊C4C2312yes—
92C32×C22⋊C4—21no—
93C32×C42—21no—
94C3×#217—21no—
95C3×#217—22no—
96C3×#216—22no—
97C3×#215—22no—
98C3×#214—22no—
99C3×#213—22no—
100C3×(C2×D3)⋊C4—22no—
101C3×(C2×D3)⋊C4—22no—
102C3×(C2×D3)⋊C4—22no—
103C3×C4⋊Dic3—22no—
104C3×C4⋊Dic3C2312yes—
105C3×Dic3⋊C4—22no—
106C3×C4×Dic3—21no—
107C2×C3×C3⋊C8D414yescomplemented
108C2×C3×C3⋊C8C2311yescharacteristic
109C2×C3×C3⋊C8C2311yescharacteristic
110C3×ΓL(1,𝔽25)—24no—
111C3×ΓL(1,𝔽25)—24no—
112#3054—31noSylow
113C2×C3×#41—21no—
114C2×C3×#41—31no—
115C2×C3×#41C2×D311yescharacteristic
116C2×C3×#41C22×C311yescharacteristic
117C23×C3×C4—31no—
118C2×#235C22×C311yescharacteristic
119C22×C4×D3C22×C311yescharacteristic
120C3×#135—64no—
121C2×C3×Q16—31no—
122C2×C3×SD16—31no—
123C2×C3×SD16—31no—
124C2×C3×D8—31no—
125C2×C3×M16—32no—
126C2×C3×M16—32no—
127C2×C3×M16—64no—
128C22×C3×C8—21no—
129C22×C3×C8—31no—
130C22×C3×C8C2×D311yescharacteristic
131C22×C3×C8C22×C311yescharacteristic
132C3×#123—61no—
133C3×#123—61no—
134C3×C22⋊Q8—32no—
135C3×C22⋊Q8—32no—
136C3×#121—32no—
137C3×#121—32no—
138C3×#120—61no—
139C3×#120—61no—
140C3×C4×D4—62no—
141C3×C4×D4—62no—
142C3×#117—21no—
143C3×#117—31no—
144C3×#117C2×D311yescharacteristic
145C3×#117C22×C311yescharacteristic
146#950—24no—
147#946C22×C312yes—
148C2×#216C22×C311yescharacteristic, complemented
149C2×#215C22×C311yescharacteristic, complemented
150#938C22×C312yes—
151#937—21no—
152#935—21no—
153C2×#214C22×C311yescharacteristic, complemented
154C2×#213C22×C311yescharacteristic, complemented
155C4×#67—22no—
156#926C22×C311yescharacteristic
157C22×C3⋊C8C22×C311yescharacteristic
158C2×ΓL(1,𝔽25)—24no—
159C2×ΓL(1,𝔽25)C22×C312yes—
160C2×ΓL(1,𝔽25)C22×C312yes—
161#897C22×C312yes—
162#895C22×C312yes—
163#886—21no—
164#882—21no—
165C4×D12—22no—
166C3×#107—32no—
167C3×#106—32no—
168C3×#103—22no—
169C3×#103—32no—
170C3×#103C2×D312yescomplemented
171C3×#103C22×C312yescomplemented
172C3×#102—22no—
173C3×#102—32no—
174C3×#102C2×D312yescomplemented
175C3×#102C22×C312yescomplemented
176#821C22×C312yescomplemented
177#816C22×C312yescomplemented
178#808C22×C312yescomplemented
179#807C22×C312yescomplemented
180C23×C32—21no—
181C23×C32C2×D411yescharacteristic
182C22×C3×D3—22no—
183C22×C3×D3—21no—
184C22×C3×D3—42no—
185C22×C3×D3C2×D412yes—
186C32×Q8—21no—
187C32×Q8—21no—
188C32×D4—21no—
189C32×D4—21no—
190C32×D4—42no—
191C2×C32×C4—21no—
192C2×C32×C4—22no—
193C2×C32×C4—42no—
194C2×C32×C4C2×D412yes—
195C2×C32×C4C2×D411yescharacteristic
196C2×C32×C4#4112yes—
197C2×C32×C4C2411yescharacteristic
198C3×#67—44no—
199C3×#67—42no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3C2×D412yes—
204C3×D12—21no—
205C3×D12—21no—
206C3×D12—44no—
207C3×C4×D3—24no—
208C3×C4×D3—22no—
209C3×C4×D3—22no—
210C3×C4×D3—42no—
211C3×Dic6—21no—
212C3×Dic6—21no—
213C32×C8—22no—
214C3×C3⋊C8C2×D412yes—
215C3×C3⋊C8C2×D412yes—
216C2×#135—31no—
217C22×M16—31no—
218#525—31no—
219#525—31no—
220#470—32no—
221#469—32no—
222#468—32no—
223#468—32no—
224#427—31no—
225#416—31no—
226#416C3×D311yescharacteristic, complemented
227C24×C3—31no—
228C23×D3C3×D411yescharacteristic
229C3×#41—24no—
230C3×#41—22no—
231C3×#41—22no—
232C3×#41—22no—
233C3×#41—22no—
234C3×#41—42no—
235C3×#41—62no—
236C3×#41—62no—
237C2×C3×Q8—21no—
238C2×C3×Q8—31no—
239C2×C3×Q8C22×D311yescharacteristic
240C2×C3×Q8C23×C311yescharacteristic
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—31no—
245C2×C3×D4—41no—
246C2×C3×D4—62no—
247C2×C3×D4—62no—
248C2×C3×D4—61no—
249C2×C3×D4C22×D311yescharacteristic
250C2×C3×D4C23×C311yescharacteristic
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—31no—
255C22×C3×C4—32no—
256C22×C3×C4—32no—
257C22×C3×C4—41no—
258C22×C3×C4—62no—
259C22×C3×C4—62no—
260C22×C3×C4—61no—
261C22×C3×C4C22×D311yescharacteristic
262C22×C3×C4C23×C311yescharacteristic
263C2×#67—21no—
264C2×#67—22no—
265C22×Dic3C3×D411yescharacteristic
266#235—22no—
267#235—22no—
268C2×D12—22no—
269C2×D12C23×C311yescharacteristic
270C2×C4×D3—22no—
271C2×C4×D3—22no—
272C2×C4×D3—21no—
273C2×C4×D3C3×D412yes—
274C2×C4×D3C23×C312yes—
275C2×Dic6C23×C311yescharacteristic
276C3×Q16—62no—
277C3×SD16—62no—
278C3×SD16—62no—
279C3×D8—62no—
280C3×M16—64no—
281C3×M16—64no—
282C2×C3×C8—22no—
283C2×C3×C8—22no—
284C2×C3×C8—22no—
285C2×C3×C8—34no—
286C2×C3×C8—31no—
287C2×C3×C8—31no—
288C2×C3×C8—42no—
289C2×C3×C8C22×D312yes—
290C2×C3×C8C23×C312yes—
291C3×C4⋊C4—22no—
292C3×C4⋊C4—32no—
293C3×C4⋊C4—62no—
294C3×C4⋊C4—62no—
295C3×C4⋊C4C22×D312yes—
296C3×C4⋊C4C23×C312yes—
297C3×C22⋊C4—21no—
298C3×C22⋊C4—21no—
299C3×C22⋊C4—41no—
300C3×C22⋊C4—62no—
301C3×C22⋊C4—62no—
302C3×C22⋊C4—62no—
303C3×C22⋊C4—62no—
304C3×C22⋊C4—61no—
305C3×C42—21no—
306C3×C42—21no—
307C3×C42—41no—
308C3×C42—61no—
309#217—21no—
310#217—22no—
311#216—22no—
312#215—22no—
313#214—22no—
314#213—22no—
315(C2×D3)⋊C4—22no—
316(C2×D3)⋊C4—22no—
317(C2×D3)⋊C4—22no—
318C4⋊Dic3—22no—
319C4⋊Dic3C23×C312yes—
320Dic3⋊C4—22no—
321C4×Dic3—21no—
322C2×C3⋊C8C3×D414yescomplemented
323C2×C3⋊C8C23×C311yescharacteristic
324C2×C3⋊C8C23×C311yescharacteristic
325ΓL(1,𝔽25)—24no—
326ΓL(1,𝔽25)—24no—
327C22×C32—22no—
328C22×C32—41no—
329C22×C32—42no—
330C22×C32#12112yes—
331C22×C32C22×D411yescharacteristic
332C2×C3×D3—22no—
333C2×C3×D3—22no—
334C2×C3×D3—22no—
335C2×C3×D3—44no—
336C2×C3×D3—41no—
337C2×C3×D3—42no—
338C32×C4—41no—
339C32×C4—42no—
340C32×C4#12112yes—
341C32×C4C22×D411yescharacteristic
342C32×C4C2×#4111yescharacteristic
343C3×Dic3—22no—
344C3×Dic3—41no—
345C3×Dic3—42no—
346C2×#41—31no—
347C2×#41C2×C3×D311yescharacteristic
348C23×C4—31no—
349#135—64no—
350C2×Q16—31no—
351C2×SD16—31no—
352C2×SD16—31no—
353C2×D8—31no—
354C2×M16—32no—
355C2×M16—32no—
356C2×M16—64no—
357C22×C8—31no—
358C22×C8C2×C3×D311yescharacteristic
359#123—61no—
360#123—61no—
361C22⋊Q8—32no—
362C22⋊Q8—32no—
363#121—32no—
364#121—32no—
365#120—61no—
366#120—61no—
367C4×D4—62no—
368C4×D4—62no—
369#117—31no—
370#117C2×C3×D311yescharacteristic
371#107—32no—
372#106—32no—
373#103—32no—
374#103C2×C3×D312yescomplemented
375#102—32no—
376#102C2×C3×D312yescomplemented
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—32no—
381C23×C3—41no—
382C23×C3—62no—
383C23×C3—61no—
384C23×C3—122no—
385C23×C3D3×D411yescharacteristic
386C23×C3C2×C3×D411yescharacteristic
387C22×D3—22no—
388C22×D3—21no—
389C22×D3—42no—
390C22×D3C2×C3×D412yes—
391C3×Q8—22no—
392C3×Q8—21no—
393C3×Q8—21no—
394C3×Q8—21no—
395C3×Q8—21no—
396C3×Q8—41no—
397C3×Q8—61no—
398C3×Q8—61no—
399C3×D4—22no—
400C3×D4—21no—
401C3×D4—21no—
402C3×D4—21no—
403C3×D4—21no—
404C3×D4—41no—
405C3×D4—44no—
406C3×D4—42no—
407C3×D4—42no—
408C3×D4—61no—
409C3×D4—61no—
410C3×D4—124no—
411C3×D4—124no—
412C3×D4—122no—
413C2×C3×C4—22no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—22no—
417C2×C3×C4—21no—
418C2×C3×C4—22no—
419C2×C3×C4—21no—
420C2×C3×C4—22no—
421C2×C3×C4—32no—
422C2×C3×C4—41no—
423C2×C3×C4—42no—
424C2×C3×C4—44no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—62no—
428C2×C3×C4—64no—
429C2×C3×C4—62no—
430C2×C3×C4—62no—
431C2×C3×C4—62no—
432C2×C3×C4—61no—
433C2×C3×C4—122no—
434C2×C3×C4#23512yes—
435C2×C3×C4D3×D412yes—
436C2×C3×C4D3×D411yescharacteristic
437C2×C3×C4C2×C3×D411yescharacteristic
438C2×C3×C4C2×C3×D412yes—
439C2×C3×C4C3×#4112yes—
440C2×C3×C4C23×D311yescharacteristic
441C2×C3×C4C24×C311yescharacteristic
442#67—44no—
443#67—42no—
444C2×Dic3—22no—
445C2×Dic3—22no—
446C2×Dic3—21no—
447C2×Dic3C2×C3×D412yes—
448D12—21no—
449D12—21no—
450D12—44no—
451C4×D3—24no—
452C4×D3—22no—
453C4×D3—22no—
454C4×D3—42no—
455Dic6—21no—
456Dic6—21no—
457C3×C8—22no—
458C3×C8—22no—
459C3×C8—32no—
460C3×C8—32no—
461C3×C8—42no—
462C3⋊C8C2×C3×D412yes—
463C3⋊C8C2×C3×D412yes—
464C2×C32—22no—
465C2×C32—81no—
466C2×C32C2×#12111yescharacteristic
467C2×C32#57512yes—
468C3×D3—42no—
469C3×D3—81no—
470C24—31no—
471#41—22no—
472#41—22no—
473#41—62no—
474#41—62no—
475C2×Q8—31no—
476C2×Q8C22×C3×D311yescharacteristic
477C2×D4—21no—
478C2×D4—31no—
479C2×D4—62no—
480C2×D4—62no—
481C2×D4—61no—
482C2×D4C22×C3×D311yescharacteristic
483C22×C4—21no—
484C22×C4—31no—
485C22×C4—32no—
486C22×C4—32no—
487C22×C4—62no—
488C22×C4—62no—
489C22×C4—61no—
490C22×C4C22×C3×D311yescharacteristic
491Q16—62no—
492SD16—62no—
493SD16—62no—
494D8—62no—
495M16—64no—
496M16—64no—
497C2×C8—22no—
498C2×C8—31no—
499C2×C8—31no—
500C2×C8—34no—
501C2×C8C22×C3×D312yes—
502C4⋊C4—32no—
503C4⋊C4—62no—
504C4⋊C4—62no—
505C4⋊C4C22×C3×D312yes—
506C22⋊C4—21no—
507C22⋊C4—62no—
508C22⋊C4—62no—
509C22⋊C4—62no—
510C22⋊C4—62no—
511C22⋊C4—61no—
512C42—21no—
513C42—61no—
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—21no—
518C22×C3—42no—
519C22×C3—42no—
520C22×C3—42no—
521C22×C3—41no—
522C22×C3—42no—
523C22×C3—41no—
524C22×C3—62no—
525C22×C3—62no—
526C22×C3—62no—
527C22×C3—82no—
528C22×C3—124no—
529C22×C3—121no—
530C22×C3—122no—
531C22×C3#88412yes—
532C22×C3C3×#12112yes—
533C22×C3C2×D3×D411yescharacteristic
534C22×C3C22×C3×D411yescharacteristic
535C2×D3—22no—
536C2×D3—22no—
537C2×D3—22no—
538C2×D3—44no—
539C2×D3—42no—
540C2×D3—41no—
541C3×C4—22no—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—42no—
545C3×C4—42no—
546C3×C4—41no—
547C3×C4—42no—
548C3×C4—41no—
549C3×C4—62no—
550C3×C4—82no—
551C3×C4—121no—
552C3×C4—122no—
553C3×C4#88412yes—
554C3×C4C3×#12112yes—
555C3×C4C2×#23511yescharacteristic
556C3×C4C2×D3×D411yescharacteristic
557C3×C4C22×C3×D411yescharacteristic
558C3×C4C2×C3×#4111yescharacteristic
559Dic3—22no—
560Dic3—42no—
561Dic3—41no—
562C32#305411yescharacteristic, complemented, Sylow
563C23—21no—
564C23—32no—
565C23—62no—
566C23—61no—
567C23—122no—
568C23C3×D3×D411yescharacteristic
569Q8—21no—
570Q8—21no—
571Q8—61no—
572Q8—61no—
573D4—21no—
574D4—21no—
575D4—42no—
576D4—61no—
577D4—61no—
578D4—124no—
579D4—124no—
580D4—122no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—32no—
584C2×C4—42no—
585C2×C4—62no—
586C2×C4—64no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—62no—
590C2×C4—61no—
591C2×C4—122no—
592C2×C4C3×#23512yes—
593C2×C4C3×D3×D411yescharacteristic
594C2×C4C3×D3×D412yes—
595C2×C4C23×C3×D311yescharacteristic
596C8—22no—
597C8—32no—
598C8—32no—
599C2×C3—22no—
600C2×C3—22no—
601C2×C3—21no—
602C2×C3—22no—
603C2×C3—42no—
604C2×C3—82no—
605C2×C3—81no—
606C2×C3—81no—
607C2×C3—122no—
608C2×C3—241no—
609C2×C3C2×#88411yescharacteristic
610C2×C3#576812yes—
611C2×C3C2×C3×#12111yescharacteristic
612C2×C3C3×#57512yes—
613D3—42no—
614D3—81no—
615C22—22no—
616C22—41no—
617C22—42no—
618C22—62no—
619C22—62no—
620C22—62no—
621C22—124no—
622C22—121no—
623C22—122no—
624C22C3×#88412yes—
625C22C2×C3×D3×D411yescharacteristic
626C4—41no—
627C4—42no—
628C4—62no—
629C4—121no—
630C4—122no—
631C4C3×#88412yes—
632C4C2×C3×#23511yescharacteristic
633C4C2×C3×D3×D411yescharacteristic
634C3—21no—
635C3#7883911yescharacteristic, direct product factor
636C3C3×#305411yescharacteristic, complemented
637C2—22no—
638C2—81no—
639C2—122no—
640C2—241no—
641C2C2×C3×#88411yescharacteristic
642C2C3×#576812yes—
subgroupG/H
centerC2×C3×C4D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#416C2
socleC22×C32C22×D4
hypercenterC3×#416D3
hypocenterC3C3×#3054
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C3×#416

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#5828C2semidirect
2. C2×C3×#950C2semidirect
3. C22×C3×ΓL(1,𝔽25)C2semidirect
4. C3×#5524C2semidirect
5. C32×#416C2semidirect
6. C3×#5113C2semidirect
7. C3×#4998C2semidirect
8. C3×#4816C2semidirect
9. C3×#4812C2semidirect
10. C3×#4782C2semidirect
11. C3×#4780C2semidirect
13. #78839C3direct (N × H)
21. C2×C3×#216C22semidirect
22. C2×C3×#215C22semidirect
26. C2×C3×#214C22semidirect
27. C2×C3×#213C22semidirect
39. C32×#103C22semidirect
40. C32×#102C22semidirect
41. C3×#821C22semidirect
42. C3×#816C22semidirect
43. C3×#808C22semidirect
44. C3×#807C22semidirect
49. #5828C2×C3semidirect
50. C2×#950C2×C3semidirect
51. C22×ΓL(1,𝔽25)C2×C3semidirect
52. #5524C2×C3semidirect
60. C3×#416D3semidirect
61. C3×#416C2×C3semidirect
62. #5113C2×C3semidirect
63. #4998C2×C3semidirect
64. #4816C2×C3semidirect
65. #4812C2×C3semidirect
66. #4782C2×C3semidirect
67. #4780C2×C3semidirect
107. C2×C3×C3⋊C8D4semidirect
148. C2×#216C22×C3semidirect
149. C2×#215C22×C3semidirect
153. C2×#214C22×C3semidirect
154. C2×#213C22×C3semidirect
170. C3×#103C2×D3semidirect
171. C3×#103C22×C3semidirect
174. C3×#102C2×D3semidirect
175. C3×#102C22×C3semidirect
176. #821C22×C3semidirect
177. #816C22×C3semidirect
178. #808C22×C3semidirect
179. #807C22×C3semidirect
226. #416C3×D3semidirect
322. C2×C3⋊C8C3×D4semidirect
374. #103C2×C3×D3semidirect
376. #102C2×C3×D3semidirect
562. C32#3054semidirect
635. C3#78839direct (N × H)
636. C3C3×#3054semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#58282
C2×C3×#9502
C22×C3×ΓL(1,𝔽25)2
C3×#55242
C32×#4162
C3×#51132
C3×#49982
C3×#48162
C3×#48122
C3×#47822
C3×#47802
C3×#30543
#788393