Finite Group Databasebeta

← #10588345⋊C3 #13141387

Subgroups — #10588345⋊C3 #13141387

Order 1728.

896 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊AGL(1,ℤ/9)C211yesmaximal, characteristic
2C22×C4×AGL(1,ℤ/9)C211yesmaximal, characteristic, complemented
3C2×(C2×AGL(1,ℤ/9))⋊C4C211yesmaximal, characteristic, complemented
4C2×(C2×AGL(1,ℤ/9))⋊C4C211yesmaximal, characteristic, complemented
5C2×(C2×AGL(1,ℤ/9))⋊C4C211yesmaximal, characteristic, complemented
63−1+2×#95C211yesmaximal, characteristic, complemented
73−1+2⋊#95C211yesmaximal, characteristic, complemented
8C3×#4665—31nomaximal
9#10588345C311yesmaximal, characteristic, complemented
10C23×AGL(1,ℤ/9)C2211yescharacteristic
11C23×AGL(1,ℤ/9)C2211yescharacteristic
12C22×C4×3−1+2C2211yescharacteristic
13C22×C4×3−1+2C2211yescharacteristic
14C22×C4×3−1+2C2211yescharacteristic
15C22×3−1+2⋊C4C2211yescharacteristic
16C22×3−1+2⋊C4C2211yescharacteristic
17C2×C4⋊AGL(1,ℤ/9)—22no—
18C2×C4⋊AGL(1,ℤ/9)—22no—
19C2×C4⋊AGL(1,ℤ/9)C414yescomplemented
20C2×C4×AGL(1,ℤ/9)—22no—
21C2×C4×AGL(1,ℤ/9)—22no—
22C2×C4×AGL(1,ℤ/9)—22no—
23(C2×AGL(1,ℤ/9))⋊C4—22no—
24(C2×AGL(1,ℤ/9))⋊C4—22no—
25(C2×AGL(1,ℤ/9))⋊C4—22no—
26C22×C3×D12—31no—
27C22×C3×C4×D3—31no—
28C2×C3×(C2×D3)⋊C4—31no—
29C2×C3×(C2×D3)⋊C4—31no—
30C2×C3×(C2×D3)⋊C4—31no—
31C22×D36C2×C311yescharacteristic
32C22×C4×D9C2×C311yescharacteristic, complemented
33C32×#95D311yescharacteristic
34C3×C3⋊#95—31no—
35C2×(C2×D9)⋊C4C2×C311yescharacteristic, complemented
36C2×(C2×D9)⋊C4C2×C311yescharacteristic, complemented
37C2×(C2×D9)⋊C4C2×C311yescharacteristic, complemented
38C9×#95—21no—
39C9×#95C2×C311yescharacteristic, complemented
40C9⋊#95C2×C311yescharacteristic, complemented
41C23×3−1+2C2311yescharacteristic
42C22×AGL(1,ℤ/9)—21no—
43C22×AGL(1,ℤ/9)—21no—
44C22×AGL(1,ℤ/9)—21no—
45C22×AGL(1,ℤ/9)—21no—
46C22×AGL(1,ℤ/9)—21no—
47C22×AGL(1,ℤ/9)—21no—
48C22×AGL(1,ℤ/9)—21no—
49C22×AGL(1,ℤ/9)—21no—
50C22×AGL(1,ℤ/9)—21no—
51C22×AGL(1,ℤ/9)—21no—
52C22×AGL(1,ℤ/9)C2×C412yes—
53C22×AGL(1,ℤ/9)C2×C412yescomplemented
54C22×AGL(1,ℤ/9)D412yes—
55C22×AGL(1,ℤ/9)D412yes—
56C2×C4×3−1+2—21no—
57C2×C4×3−1+2—21no—
58C2×C4×3−1+2—21no—
59C2×C4×3−1+2—21no—
60C2×C4×3−1+2—21no—
61C2×C4×3−1+2—21no—
62C2×C4×3−1+2—21no—
63C2×C4×3−1+2C2×C412yescomplemented
64C2×C4×3−1+2D412yescomplemented
65C2×3−1+2⋊C4—21no—
66C2×3−1+2⋊C4—21no—
67C2×3−1+2⋊C4—21no—
68C2×3−1+2⋊C4—21no—
69C2×3−1+2⋊C4—21no—
70C2×3−1+2⋊C4D412yescomplemented
71C4⋊AGL(1,ℤ/9)—28no—
72C4×AGL(1,ℤ/9)—28no—
73C3×#386—91no—
74#4665—31no—
75C23×C3×D3—31no—
76C23×C3×D3—31no—
77C22×C32×C4C2×D311yescharacteristic
78C22×C32×C4C2×D311yescharacteristic
79C22×C32×C4C2×D311yescharacteristic
80C22×C3×Dic3—31no—
81C22×C3×Dic3—31no—
82C2×C3×D12—34no—
83C2×C3×D12—62no—
84C2×C3×D12—62no—
85C2×C3×C4×D3—62no—
86C2×C3×C4×D3—62no—
87C2×C3×C4×D3—62no—
88C23×D9C22×C311yescharacteristic
89C23×D9C22×C311yescharacteristic
90C3×(C2×D3)⋊C4—62no—
91C3×(C2×D3)⋊C4—62no—
92C3×(C2×D3)⋊C4—62no—
93C22×C4×C9—21no—
94C22×C4×C9—21no—
95C22×C4×C9—21no—
96C22×C4×C9C22×C311yescharacteristic
97C22×C4×C9C22×C311yescharacteristic
98C22×C4×C9C22×C311yescharacteristic
99C22×Dic9C22×C311yescharacteristic
100C22×Dic9C22×C311yescharacteristic
101C2×D36—22no—
102C2×D36—22no—
103C2×D36C3×C414yescomplemented
104C2×C4×D9—22no—
105C2×C4×D9—22no—
106C2×C4×D9—22no—
107(C2×D9)⋊C4—22no—
108(C2×D9)⋊C4—22no—
109(C2×D9)⋊C4—22no—
110C22×3−1+2C22×C411yescharacteristic
111C22×3−1+2C2×D411yescharacteristic
112C22×3−1+2C2×D411yescharacteristic
113C22×3−1+2C2×D411yescharacteristic
114C22×3−1+2C2×D411yescharacteristic
115C22×3−1+2#4111yescharacteristic
116C22×3−1+2#4111yescharacteristic
117C2×AGL(1,ℤ/9)—22no—
118C2×AGL(1,ℤ/9)—22no—
119C2×AGL(1,ℤ/9)—22no—
120C2×AGL(1,ℤ/9)—22no—
121C2×AGL(1,ℤ/9)—22no—
122C2×AGL(1,ℤ/9)—22no—
123C2×AGL(1,ℤ/9)—22no—
124C2×AGL(1,ℤ/9)—22no—
125C2×AGL(1,ℤ/9)—22no—
126C2×AGL(1,ℤ/9)—41no—
127C2×AGL(1,ℤ/9)—41no—
128C2×AGL(1,ℤ/9)—41no—
129C2×AGL(1,ℤ/9)—41no—
130C2×AGL(1,ℤ/9)C22⋊C414yescomplemented
131C4×3−1+2—22no—
132C4×3−1+2—22no—
133C4×3−1+2—41no—
1343−1+2⋊C4—22no—
1353−1+2⋊C4—41no—
136C22×C3×D4—91no—
137C23×C3×C4—91no—
138C22×D12—31no—
139C22×C4×D3—31no—
140C2×C3×C22⋊C4—91no—
141C2×C3×C22⋊C4—91no—
142C2×C3×C22⋊C4—91no—
143C2×(C2×D3)⋊C4—31no—
144C2×(C2×D3)⋊C4—31no—
145C2×(C2×D3)⋊C4—31no—
146C3×#95—31no—
147C3×#95—91no—
148C3×#95C3×D311yescharacteristic
149C3⋊#95—31no—
150C23×C32C22×D311yescharacteristic
151C22×C3×D3—32no—
152C22×C3×D3—32no—
153C22×C3×D3—32no—
154C22×C3×D3—32no—
155C22×C3×D3—61no—
156C22×C3×D3—61no—
157C22×C3×D3—61no—
158C22×C3×D3—61no—
159C22×C3×D3—61no—
160C22×C3×D3—61no—
161C22×C3×D3—61no—
162C22×C3×D3—61no—
163C22×C3×D3—61no—
164C22×C3×D3—61no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4C4×D312yes—
173C2×C32×C4D1212yes—
174C2×C3×Dic3—32no—
175C2×C3×Dic3—61no—
176C2×C3×Dic3—61no—
177C2×C3×Dic3—61no—
178C2×C3×Dic3—61no—
179C2×C3×Dic3—61no—
180C3×D12—68no—
181C3×C4×D3—68no—
182C23×C9—21no—
183C23×C9C23×C311yescharacteristic
184C22×D9—21no—
185C22×D9—21no—
186C22×D9—21no—
187C22×D9—21no—
188C22×D9—21no—
189C22×D9—21no—
190C22×D9—21no—
191C22×D9—21no—
192C22×D9—21no—
193C22×D9—21no—
194C22×D9C2×C3×C412yes—
195C22×D9C2×C3×C412yescomplemented
196C22×D9C3×D412yes—
197C22×D9C3×D412yes—
198C2×C4×C9—21no—
199C2×C4×C9—21no—
200C2×C4×C9—21no—
201C2×C4×C9—21no—
202C2×C4×C9—22no—
203C2×C4×C9—21no—
204C2×C4×C9—21no—
205C2×C4×C9—21no—
206C2×C4×C9—22no—
207C2×C4×C9—22no—
208C2×C4×C9—41no—
209C2×C4×C9—41no—
210C2×C4×C9—41no—
211C2×C4×C9—41no—
212C2×C4×C9—41no—
213C2×C4×C9—41no—
214C2×C4×C9C2×C3×C412yescomplemented
215C2×C4×C9C3×D412yescomplemented
216C2×Dic9—21no—
217C2×Dic9—21no—
218C2×Dic9—21no—
219C2×Dic9—21no—
220C2×Dic9—21no—
221C2×Dic9C3×D412yescomplemented
222D36—28no—
223C4×D9—28no—
224#386—91noSylow
225C2×3−1+2C2×C22⋊C411yescharacteristic
226C2×3−1+2C4×D411yescharacteristic
227C2×3−1+2C4×D411yescharacteristic
228C2×3−1+2#12011yescharacteristic
229C2×3−1+2#12111yescharacteristic
230C2×3−1+2#12111yescharacteristic
231C2×3−1+2#12311yescharacteristic
232AGL(1,ℤ/9)—24no—
233AGL(1,ℤ/9)—42no—
234C24×C3—91no—
235C24×C3—91no—
236C23×D3—31no—
237C23×D3—31no—
238C2×C3×D4—94no—
239C2×C3×D4—182no—
240C2×C3×D4—182no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×C3×C4—31no—
244C22×C3×C4—91no—
245C22×C3×C4—91no—
246C22×C3×C4—182no—
247C22×C3×C4—182no—
248C22×C3×C4—182no—
249C22×C3×C4C2×C3×D311yescharacteristic
250C22×C3×C4C2×C3×D311yescharacteristic
251C22×C3×C4C2×C3×D311yescharacteristic
252C22×Dic3—31no—
253C22×Dic3—31no—
254C2×D12—34no—
255C2×D12—62no—
256C2×D12—62no—
257C2×C4×D3—62no—
258C2×C4×D3—62no—
259C2×C4×D3—62no—
260C3×C22⋊C4—182no—
261C3×C22⋊C4—182no—
262C3×C22⋊C4—182no—
263(C2×D3)⋊C4—62no—
264(C2×D3)⋊C4—62no—
265(C2×D3)⋊C4—62no—
266C22×C32C2×C4×D311yescharacteristic
267C22×C32C2×D1211yescharacteristic
268C22×C32#23511yescharacteristic
269C22×C32D3×D411yescharacteristic
270C22×C32D3×D411yescharacteristic
271C22×C32D3×D411yescharacteristic
272C22×C32#23911yescharacteristic
273C2×C3×D3—34no—
274C2×C3×D3—62no—
275C2×C3×D3—62no—
276C2×C3×D3—62no—
277C2×C3×D3—62no—
278C2×C3×D3—62no—
279C2×C3×D3—62no—
280C2×C3×D3—62no—
281C2×C3×D3—62no—
282C2×C3×D3—62no—
283C2×C3×D3—121no—
284C2×C3×D3—121no—
285C2×C3×D3—121no—
286C2×C3×D3—121no—
287C32×C4—22no—
288C32×C4—22no—
289C32×C4—41no—
290C3×Dic3—62no—
291C3×Dic3—121no—
292C22×C9—21no—
293C22×C9—21no—
294C22×C9—21no—
295C22×C9—21no—
296C22×C9—21no—
297C22×C9—21no—
298C22×C9—21no—
299C22×C9C22×C3×C411yescharacteristic
300C22×C9C2×C3×D411yescharacteristic
301C22×C9C2×C3×D411yescharacteristic
302C22×C9C2×C3×D411yescharacteristic
303C22×C9C2×C3×D411yescharacteristic
304C22×C9C3×#4111yescharacteristic
305C22×C9C3×#4111yescharacteristic
306C2×D9—22no—
307C2×D9—22no—
308C2×D9—22no—
309C2×D9—22no—
310C2×D9—22no—
311C2×D9—22no—
312C2×D9—22no—
313C2×D9—22no—
314C2×D9—22no—
315C2×D9—41no—
316C2×D9—41no—
317C2×D9—41no—
318C2×D9—41no—
319C2×D9C3×C22⋊C414yescomplemented
320C4×C9—22no—
321C4×C9—22no—
322C4×C9—42no—
323C4×C9—42no—
324C4×C9—42no—
325C4×C9—41no—
326Dic9—22no—
327Dic9—41no—
328C22×D4—91no—
329C23×C4—91no—
330C2×C22⋊C4—91no—
331C2×C22⋊C4—91no—
332C2×C22⋊C4—91no—
333#95—91no—
334#95AGL(1,ℤ/9)11yescharacteristic, complemented
3353−1+2#38611yescharacteristic, complemented, Sylow
336C23×C3—31no—
337C23×C3—92no—
338C23×C3—92no—
339C23×C3—92no—
340C23×C3—92no—
341C23×C3—181no—
342C23×C3—181no—
343C23×C3—181no—
344C23×C3—181no—
345C23×C3—181no—
346C23×C3—181no—
347C23×C3—181no—
348C23×C3—181no—
349C23×C3—181no—
350C23×C3—181no—
351C23×C3C22×C3×D311yescharacteristic
352C22×D3—32no—
353C22×D3—32no—
354C22×D3—32no—
355C22×D3—32no—
356C22×D3—61no—
357C22×D3—61no—
358C22×D3—61no—
359C22×D3—61no—
360C22×D3—61no—
361C22×D3—61no—
362C22×D3—61no—
363C22×D3—61no—
364C22×D3—61no—
365C22×D3—61no—
366C3×D4—188no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—32no—
375C2×C3×C4—32no—
376C2×C3×C4—61no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—61no—
380C2×C3×C4—61no—
381C2×C3×C4—61no—
382C2×C3×C4—61no—
383C2×C3×C4—92no—
384C2×C3×C4—188no—
385C2×C3×C4—181no—
386C2×C3×C4—181no—
387C2×C3×C4—181no—
388C2×C3×C4—181no—
389C2×C3×C4—181no—
390C2×C3×C4C3×C4×D312yes—
391C2×C3×C4C3×D1212yes—
392C2×Dic3—32no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398D12—68no—
399C4×D3—68no—
400C2×C32C4×D1211yescharacteristic
401C2×C32D3×C22⋊C411yescharacteristic
402C2×C32#88211yescharacteristic
403C2×C32#88411yescharacteristic
404C2×C32#89311yescharacteristic
405C2×C32#89411yescharacteristic
406C2×C32#89511yescharacteristic
407C3×D3—64no—
408C3×D3—122no—
409C2×C9—21no—
410C2×C9—21no—
411C2×C9—21no—
412C2×C9—21no—
413C2×C9—21no—
414C2×C9—21no—
415C2×C9—21no—
416C2×C9C2×C3×C22⋊C411yescharacteristic
417C2×C9C3×C4×D411yescharacteristic
418C2×C9C3×C4×D411yescharacteristic
419C2×C9C3×#12011yescharacteristic
420C2×C9C3×#12111yescharacteristic
421C2×C9C3×#12111yescharacteristic
422C2×C9C3×#12311yescharacteristic
423D9—24no—
424D9—42no—
425C24—91no—
426C24—91no—
427C2×D4—94no—
428C2×D4—182no—
429C2×D4—182no—
430C22×C4—91no—
431C22×C4—91no—
432C22×C4—182no—
433C22×C4—182no—
434C22×C4—182no—
435C22×C4C2×AGL(1,ℤ/9)11yescharacteristic
436C22×C4C2×AGL(1,ℤ/9)11yescharacteristic
437C22×C4C2×AGL(1,ℤ/9)11yescharacteristic
438C22⋊C4—182no—
439C22⋊C4—182no—
440C22⋊C4—182no—
441C22×C3—31no—
442C22×C3—31no—
443C22×C3—31no—
444C22×C3—31no—
445C22×C3—31no—
446C22×C3—31no—
447C22×C3—31no—
448C22×C3—94no—
449C22×C3—182no—
450C22×C3—182no—
451C22×C3—182no—
452C22×C3—182no—
453C22×C3—182no—
454C22×C3—182no—
455C22×C3—182no—
456C22×C3—182no—
457C22×C3—182no—
458C22×C3—361no—
459C22×C3—361no—
460C22×C3—361no—
461C22×C3—361no—
462C22×C3C2×C3×C4×D311yescharacteristic
463C22×C3C2×C3×D1211yescharacteristic
464C22×C3C3×#23511yescharacteristic
465C22×C3C3×D3×D411yescharacteristic
466C22×C3C3×D3×D411yescharacteristic
467C22×C3C3×D3×D411yescharacteristic
468C22×C3C3×#23911yescharacteristic
469C2×D3—34no—
470C2×D3—62no—
471C2×D3—62no—
472C2×D3—62no—
473C2×D3—62no—
474C2×D3—62no—
475C2×D3—62no—
476C2×D3—62no—
477C2×D3—62no—
478C2×D3—62no—
479C2×D3—121no—
480C2×D3—121no—
481C2×D3—121no—
482C2×D3—121no—
483C3×C4—22no—
484C3×C4—22no—
485C3×C4—41no—
486C3×C4—62no—
487C3×C4—62no—
488C3×C4—121no—
489C3×C4—182no—
490C3×C4—361no—
491Dic3—62no—
492Dic3—121no—
493C32#466511yescharacteristic
494C9—21no—
495C9C3×#38611yescharacteristic, complemented
496C23—92no—
497C23—92no—
498C23—92no—
499C23—92no—
500C23—181no—
501C23—181no—
502C23—181no—
503C23—181no—
504C23—181no—
505C23—181no—
506C23—181no—
507C23—181no—
508C23—181no—
509C23—181no—
510C23C22×AGL(1,ℤ/9)11yescharacteristic
511D4—188no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—92no—
520C2×C4—188no—
521C2×C4—181no—
522C2×C4—181no—
523C2×C4—181no—
524C2×C4—181no—
525C2×C4—181no—
526C2×C4C4×AGL(1,ℤ/9)12yescomplemented
527C2×C4C4⋊AGL(1,ℤ/9)12yescomplemented
528C2×C3—31no—
529C2×C3—31no—
530C2×C3—31no—
531C2×C3—31no—
532C2×C3—31no—
533C2×C3—31no—
534C2×C3—31no—
535C2×C3—184no—
536C2×C3—362no—
537C2×C3C3×C4×D1211yescharacteristic
538C2×C3C3×D3×C22⋊C411yescharacteristic
539C2×C3C3×#88211yescharacteristic
540C2×C3C3×#88411yescharacteristic
541C2×C3C3×#89311yescharacteristic
542C2×C3C3×#89411yescharacteristic
543C2×C3C3×#89511yescharacteristic
544D3—64no—
545D3—122no—
546C22—94no—
547C22—182no—
548C22—182no—
549C22—182no—
550C22—182no—
551C22—182no—
552C22—182no—
553C22—182no—
554C22—182no—
555C22—182no—
556C22—361no—
557C22—361no—
558C22—361no—
559C22—361no—
560C22C2×C4×AGL(1,ℤ/9)11yescharacteristic
561C22C2×C4⋊AGL(1,ℤ/9)11yescharacteristic
562C22#3697⋊C311yescharacteristic
563C22D4×AGL(1,ℤ/9)11yescharacteristic
564C22D4×AGL(1,ℤ/9)11yescharacteristic
565C22D4×AGL(1,ℤ/9)11yescharacteristic
566C22#8872411yescharacteristic
567C4—22no—
568C4—22no—
569C4—41no—
570C4—182no—
571C4—361no—
572C3—31no—
573C3C3×#466511yescharacteristic
574C2—184no—
575C2—362no—
576C2C4×C4⋊AGL(1,ℤ/9)11yescharacteristic
577C2C22⋊C4×AGL(1,ℤ/9)11yescharacteristic
578C2#63444⋊C311yescharacteristic
579C2#63446⋊C311yescharacteristic
580C2#63455⋊C311yescharacteristic
581C2#63456⋊C311yescharacteristic
582C2#63457⋊C311yescharacteristic
subgroupG/H
centerC23C22×AGL(1,ℤ/9)
commutatorC22×C9C22×C3×C4
Frattini, socleC23×C3C22×C3×D3
Fitting3−1+2×#95C2
prime radicalC22×C4⋊AGL(1,ℤ/9)C2
cosocleC23×C9C23×C3
hypercenter#95AGL(1,ℤ/9)
hypocenterC9C3×#386
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C22×C4×AGL(1,ℤ/9)C2semidirect
3. C2×(C2×AGL(1,ℤ/9))⋊C4C2semidirect
4. C2×(C2×AGL(1,ℤ/9))⋊C4C2semidirect
5. C2×(C2×AGL(1,ℤ/9))⋊C4C2semidirect
6. 3−1+2×#95C2semidirect
7. 3−1+2⋊#95C2semidirect
9. #10588345C3semidirect
19. C2×C4⋊AGL(1,ℤ/9)C4semidirect
32. C22×C4×D9C2×C3semidirect
35. C2×(C2×D9)⋊C4C2×C3semidirect
36. C2×(C2×D9)⋊C4C2×C3semidirect
37. C2×(C2×D9)⋊C4C2×C3semidirect
39. C9×#95C2×C3semidirect
40. C9⋊#95C2×C3semidirect
53. C22×AGL(1,ℤ/9)C2×C4semidirect
63. C2×C4×3−1+2C2×C4semidirect
64. C2×C4×3−1+2D4semidirect
70. C2×3−1+2⋊C4D4semidirect
103. C2×D36C3×C4semidirect
130. C2×AGL(1,ℤ/9)C22⋊C4semidirect
195. C22×D9C2×C3×C4semidirect
214. C2×C4×C9C2×C3×C4semidirect
215. C2×C4×C9C3×D4semidirect
221. C2×Dic9C3×D4semidirect
319. C2×D9C3×C22⋊C4semidirect
334. #95AGL(1,ℤ/9)semidirect
335. 3−1+2#386semidirect
495. C9C3×#386semidirect
526. C2×C4C4×AGL(1,ℤ/9)semidirect
527. C2×C4C4⋊AGL(1,ℤ/9)semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊AGL(1,ℤ/9)2
C22×C4×AGL(1,ℤ/9)2
C2×(C2×AGL(1,ℤ/9))⋊C42
3−1+2×#952
3−1+2⋊#952
C3×#46653
#105883453