Finite Group Databasebeta

← #10592650⋊C3 #13142498

Subgroups — #10592650⋊C3 #13142498

Order 1728.

797 conjugacy classes of subgroups.

The subgroup lattice has 613 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×H(3,𝔽3)C211yesmaximal, characteristic
2C2×#3757⋊C3C211yesmaximal, characteristic
3C2×#3757⋊C3C211yesmaximal, characteristic
4C2×C4⋊((C3⋊Dic3)⋊C3)C211yesmaximal, characteristic, complemented
5C2×C4×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
6#63658⋊C3C211yesmaximal, characteristic, complemented
7#63658⋊C3C211yesmaximal, characteristic, complemented
8#10592650C311yesmaximal, characteristic, complemented
9C3×#4951—31nomaximal
10C24×H(3,𝔽3)C2211yescharacteristic
11C22×C4×H(3,𝔽3)C2211yescharacteristic
12C22×C4×H(3,𝔽3)C2211yescharacteristic
13C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
14C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
15C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
16C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
17C22⋊C4×H(3,𝔽3)C414yescomplemented
18#3757⋊C3—22no—
19#3757⋊C3—22no—
20C4⋊((C3⋊Dic3)⋊C3)—22no—
21C4×(C3⋊Dic3)⋊C3—22no—
22C2×C32×C22⋊C4—21no—
23C2×C32×C22⋊C4D311yescharacteristic
24C2×C32×C22⋊C4C2×C311yescharacteristic
25C2×#3757C2×C311yescharacteristic
26C2×#3757C2×C311yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2×C311yescharacteristic, complemented
28C2×C4×C3⋊Dic3C2×C311yescharacteristic, complemented
29C2×C3×#217—31no—
30C2×C3×#217—31no—
31C2×C3×C4⋊Dic3—31no—
32C2×C3×C4×Dic3—31no—
33#63658C2×C311yescharacteristic, complemented
34#63658C2×C311yescharacteristic, complemented
35C3×C3⋊#95—31no—
36C3×C3⋊#95—31no—
37C23×H(3,𝔽3)—21no—
38C23×H(3,𝔽3)—21no—
39C23×H(3,𝔽3)—21no—
40C23×H(3,𝔽3)—21no—
41C23×H(3,𝔽3)—21no—
42C23×H(3,𝔽3)—21no—
43C23×H(3,𝔽3)C2×C412yes—
44C23×H(3,𝔽3)C2311yescharacteristic
45C2×C4×H(3,𝔽3)—21no—
46C2×C4×H(3,𝔽3)—21no—
47C2×C4×H(3,𝔽3)—21no—
48C2×C4×H(3,𝔽3)—21no—
49C2×C4×H(3,𝔽3)C2×C412yes—
50C2×C4×H(3,𝔽3)C2×C412yes—
51C2×(C3⋊Dic3)⋊C3—21no—
52C2×(C3⋊Dic3)⋊C3—21no—
53C2×(C3⋊Dic3)⋊C3—21no—
54C2×(C3⋊Dic3)⋊C3—21no—
55C2×(C3⋊Dic3)⋊C3—21no—
56C2×(C3⋊Dic3)⋊C3—21no—
57C2×(C3⋊Dic3)⋊C3—21no—
58C2×(C3⋊Dic3)⋊C3—21no—
59C2×(C3⋊Dic3)⋊C3—21no—
60C2×(C3⋊Dic3)⋊C3—21no—
61C2×(C3⋊Dic3)⋊C3D412yes—
62C2×(C3⋊Dic3)⋊C3D412yes—
63C3×#388—91no—
64#4951—31no—
65#4951—91no—
66C24×C32—21no—
67C24×C32C2×D311yescharacteristic
68C24×C32C22×C311yescharacteristic
69C22×C32×C4—21no—
70C22×C32×C4—21no—
71C22×C32×C4C2×D311yescharacteristic
72C22×C32×C4C2×D311yescharacteristic
73C22×C32×C4C22×C311yescharacteristic
74C22×C32×C4C22×C311yescharacteristic
75C22×C3⋊Dic3C22×C311yescharacteristic
76C22×C3⋊Dic3C22×C311yescharacteristic
77C22×C3⋊Dic3C22×C311yescharacteristic
78C22×C3⋊Dic3C22×C311yescharacteristic
79C22×C3×Dic3—31no—
80C22×C3×Dic3—31no—
81C22×C3×Dic3—31no—
82C22×C3×Dic3—31no—
83C32×C22⋊C4—24no—
84C32×C22⋊C4Dic314yescomplemented
85C32×C22⋊C4C3×C414yescomplemented
86#3757—22no—
87#3757—22no—
88C4⋊(C3⋊Dic3)—22no—
89C4×C3⋊Dic3—22no—
90C3×#217—62no—
91C3×#217—62no—
92C3×C4⋊Dic3—62no—
93C3×C4×Dic3—62no—
94C22×H(3,𝔽3)—22no—
95C22×H(3,𝔽3)—22no—
96C22×H(3,𝔽3)—22no—
97C22×H(3,𝔽3)—41no—
98C22×H(3,𝔽3)—41no—
99C22×H(3,𝔽3)—41no—
100C22×H(3,𝔽3)—41no—
101C22×H(3,𝔽3)C22×C411yescharacteristic
102C22×H(3,𝔽3)C2×D411yescharacteristic
103C22×H(3,𝔽3)C2×D411yescharacteristic
104C22×H(3,𝔽3)#4111yescharacteristic
105C22×H(3,𝔽3)#4111yescharacteristic
106C22×H(3,𝔽3)#4111yescharacteristic
107C22×H(3,𝔽3)#4111yescharacteristic
108C4×H(3,𝔽3)—22no—
109C4×H(3,𝔽3)—22no—
110(C3⋊Dic3)⋊C3—22no—
111(C3⋊Dic3)⋊C3—22no—
112(C3⋊Dic3)⋊C3—41no—
113(C3⋊Dic3)⋊C3—41no—
114C2×C3×C4⋊C4—91no—
115C2×C3×C22⋊C4—31no—
116C2×C3×C22⋊C4—31no—
117C2×C3×C22⋊C4—61no—
118C2×C3×C22⋊C4—91no—
119C2×C3×C22⋊C4—91no—
120C2×C3×C22⋊C4C3×D311yescharacteristic
121C2×C3×C42—91no—
122C2×#217—31no—
123C2×#217—31no—
124C2×#217—91no—
125C2×#217—91no—
126C2×C4⋊Dic3—31no—
127C2×C4⋊Dic3—91no—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—91no—
130C3×#95—91no—
131C3×#95—91no—
132C3⋊#95—31no—
133C3⋊#95—31no—
134C3⋊#95—91no—
135C3⋊#95—91no—
136C23×C32—22no—
137C23×C32—22no—
138C23×C32—21no—
139C23×C32—21no—
140C23×C32—21no—
141C23×C32—21no—
142C23×C32—21no—
143C23×C32—21no—
144C23×C32—21no—
145C23×C32—21no—
146C23×C32—21no—
147C23×C32—21no—
148C23×C32—21no—
149C23×C32—21no—
150C23×C32—22no—
151C23×C32—21no—
152C23×C32—41no—
153C23×C32—41no—
154C23×C32—41no—
155C23×C32—41no—
156C23×C32C2×Dic312yes—
157C23×C32C2×C3×C412yes—
158C23×C32C22×D311yescharacteristic
159C23×C32C23×C311yescharacteristic
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—22no—
169C2×C32×C4—22no—
170C2×C32×C4—41no—
171C2×C32×C4—41no—
172C2×C32×C4—41no—
173C2×C32×C4—41no—
174C2×C32×C4C2×Dic312yes—
175C2×C32×C4C2×Dic312yes—
176C2×C32×C4C2×C3×C412yes—
177C2×C32×C4C2×C3×C412yes—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3C3×D412yes—
189C2×C3⋊Dic3C3×D412yes—
190C2×C3×Dic3—32no—
191C2×C3×Dic3—32no—
192C2×C3×Dic3—61no—
193C2×C3×Dic3—61no—
194C2×C3×Dic3—61no—
195C2×C3×Dic3—61no—
196C2×C3×Dic3—61no—
197C2×C3×Dic3—61no—
198C2×C3×Dic3—61no—
199C2×C3×Dic3—61no—
200C2×C3×Dic3—61no—
201C2×C3×Dic3—61no—
202#388—91noSylow
203C2×H(3,𝔽3)—42no—
204C2×H(3,𝔽3)#11711yescharacteristic
205C2×H(3,𝔽3)C4×D411yescharacteristic
206C2×H(3,𝔽3)C4×D411yescharacteristic
207C2×H(3,𝔽3)#12111yescharacteristic
208C2×H(3,𝔽3)#12311yescharacteristic
209C2×H(3,𝔽3)#12411yescharacteristic
210C2×H(3,𝔽3)#12611yescharacteristic
211C24×C3—31no—
212C24×C3—31no—
213C24×C3—61no—
214C24×C3C2×C3×D311yescharacteristic
215C22×C3×C4—31no—
216C22×C3×C4—31no—
217C22×C3×C4—31no—
218C22×C3×C4—31no—
219C22×C3×C4—61no—
220C22×C3×C4—61no—
221C22×C3×C4—91no—
222C22×C3×C4—91no—
223C22×C3×C4—91no—
224C22×C3×C4—91no—
225C22×C3×C4C2×C3×D311yescharacteristic
226C22×C3×C4C2×C3×D311yescharacteristic
227C22×Dic3—31no—
228C22×Dic3—31no—
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—91no—
232C22×Dic3—91no—
233C22×Dic3—91no—
234C22×Dic3—91no—
235C3×C4⋊C4—182no—
236C3×C22⋊C4—34no—
237C3×C22⋊C4—34no—
238C3×C22⋊C4—64no—
239C3×C22⋊C4—182no—
240C3×C22⋊C4—182no—
241C3×C22⋊C4C3×Dic314yes—
242C3×C42—182no—
243#217—62no—
244#217—62no—
245#217—182no—
246#217—182no—
247C4⋊Dic3—62no—
248C4⋊Dic3—182no—
249C4×Dic3—62no—
250C4×Dic3—182no—
251C22×C32—24no—
252C22×C32—22no—
253C22×C32—22no—
254C22×C32—22no—
255C22×C32—22no—
256C22×C32—22no—
257C22×C32—22no—
258C22×C32—21no—
259C22×C32—21no—
260C22×C32—21no—
261C22×C32—21no—
262C22×C32—21no—
263C22×C32—21no—
264C22×C32—21no—
265C22×C32—42no—
266C22×C32—42no—
267C22×C32—42no—
268C22×C32—42no—
269C22×C32—42no—
270C22×C32—42no—
271C22×C32—41no—
272C22×C32—41no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32—41no—
276C22×C32—41no—
277C22×C32—41no—
278C22×C32—41no—
279C22×C32#23511yescharacteristic
280C22×C32#23511yescharacteristic
281C22×C32D3×D411yescharacteristic
282C22×C32D3×D411yescharacteristic
283C22×C32#23711yescharacteristic
284C22×C32#23711yescharacteristic
285C22×C32C22×Dic311yescharacteristic
286C22×C32C22×C3×C411yescharacteristic
287C22×C32C2×C3×D411yescharacteristic
288C22×C32C2×C3×D411yescharacteristic
289C22×C32C3×#4111yescharacteristic
290C22×C32C3×#4111yescharacteristic
291C22×C32C3×#4111yescharacteristic
292C22×C32C3×#4111yescharacteristic
293C32×C4—22no—
294C32×C4—22no—
295C32×C4—22no—
296C32×C4—22no—
297C32×C4—42no—
298C32×C4—42no—
299C3⋊Dic3—22no—
300C3⋊Dic3—22no—
301C3⋊Dic3—41no—
302C3⋊Dic3—41no—
303C3×Dic3—62no—
304C3×Dic3—62no—
305C3×Dic3—121no—
306C3×Dic3—121no—
307C2×C4⋊C4—91no—
308C2×C22⋊C4—91no—
309C2×C22⋊C4—91no—
310C2×C22⋊C4(C3⋊D3)⋊C311yescharacteristic
311C2×C42—91no—
312#95—91no—
313#95—91no—
314H(3,𝔽3)#38811yescharacteristic, complemented, Sylow
315C23×C3—21no—
316C23×C3—21no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—21no—
320C23×C3—21no—
321C23×C3—32no—
322C23×C3—32no—
323C23×C3—31no—
324C23×C3—31no—
325C23×C3—61no—
326C23×C3—61no—
327C23×C3—61no—
328C23×C3—61no—
329C23×C3—61no—
330C23×C3—61no—
331C23×C3—61no—
332C23×C3—61no—
333C23×C3—61no—
334C23×C3—61no—
335C23×C3—61no—
336C23×C3—61no—
337C23×C3—62no—
338C23×C3—62no—
339C23×C3—62no—
340C23×C3—61no—
341C23×C3—121no—
342C23×C3—121no—
343C23×C3—121no—
344C23×C3—121no—
345C23×C3C2×C3×Dic312yes—
346C23×C3C22×C3×D311yescharacteristic
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—32no—
354C2×C3×C4—32no—
355C2×C3×C4—61no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—92no—
366C2×C3×C4—92no—
367C2×C3×C4—121no—
368C2×C3×C4—121no—
369C2×C3×C4—121no—
370C2×C3×C4—121no—
371C2×C3×C4—181no—
372C2×C3×C4—181no—
373C2×C3×C4—181no—
374C2×C3×C4—181no—
375C2×C3×C4—181no—
376C2×C3×C4—181no—
377C2×C3×C4—181no—
378C2×C3×C4—181no—
379C2×C3×C4—181no—
380C2×C3×C4—181no—
381C2×C3×C4C2×C3×Dic312yes—
382C2×C3×C4C2×C3×Dic312yes—
383C2×Dic3—32no—
384C2×Dic3—32no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—92no—
396C2×Dic3—92no—
397C2×Dic3—181no—
398C2×Dic3—181no—
399C2×Dic3—181no—
400C2×Dic3—181no—
401C2×Dic3—181no—
402C2×Dic3—181no—
403C2×Dic3—181no—
404C2×Dic3—181no—
405C2×Dic3—181no—
406C2×Dic3—181no—
407C2×C32—21no—
408C2×C32—21no—
409C2×C32—21no—
410C2×C32—21no—
411C2×C32—21no—
412C2×C32—21no—
413C2×C32—21no—
414C2×C32—44no—
415C2×C32—42no—
416C2×C32—42no—
417C2×C32#87911yescharacteristic
418C2×C32#88311yescharacteristic
419C2×C32#88411yescharacteristic
420C2×C32#88511yescharacteristic
421C2×C32#92611yescharacteristic
422C2×C32D4×Dic311yescharacteristic
423C2×C32D4×Dic311yescharacteristic
424C2×C32C3×#11711yescharacteristic
425C2×C32C3×C4×D411yescharacteristic
426C2×C32C3×C4×D411yescharacteristic
427C2×C32C3×#12111yescharacteristic
428C2×C32C3×#12311yescharacteristic
429C2×C32C3×#12411yescharacteristic
430C2×C32C3×#12611yescharacteristic
431C24C2×(C3⋊D3)⋊C311yescharacteristic
432C22×C4—91no—
433C22×C4—91no—
434C22×C4—91no—
435C22×C4—91no—
436C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
437C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
438C4⋊C4—182no—
439C22⋊C4—182no—
440C22⋊C4—182no—
441C22⋊C4(C3⋊Dic3)⋊C314yescomplemented
442C42—182no—
443C22×C3—22no—
444C22×C3—22no—
445C22×C3—22no—
446C22×C3—31no—
447C22×C3—31no—
448C22×C3—31no—
449C22×C3—31no—
450C22×C3—31no—
451C22×C3—31no—
452C22×C3—31no—
453C22×C3—31no—
454C22×C3—31no—
455C22×C3—31no—
456C22×C3—31no—
457C22×C3—31no—
458C22×C3—31no—
459C22×C3—31no—
460C22×C3—41no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—62no—
465C22×C3—62no—
466C22×C3—62no—
467C22×C3—62no—
468C22×C3—62no—
469C22×C3—62no—
470C22×C3—64no—
471C22×C3—61no—
472C22×C3—61no—
473C22×C3—61no—
474C22×C3—61no—
475C22×C3—61no—
476C22×C3—61no—
477C22×C3—61no—
478C22×C3—122no—
479C22×C3—122no—
480C22×C3—121no—
481C22×C3—121no—
482C22×C3—121no—
483C22×C3—121no—
484C22×C3—121no—
485C22×C3—121no—
486C22×C3—121no—
487C22×C3—121no—
488C22×C3—122no—
489C22×C3—122no—
490C22×C3—122no—
491C22×C3—122no—
492C22×C3C3×#23511yescharacteristic
493C22×C3C3×#23511yescharacteristic
494C22×C3C3×D3×D411yescharacteristic
495C22×C3C3×D3×D411yescharacteristic
496C22×C3C3×#23711yescharacteristic
497C22×C3C3×#23711yescharacteristic
498C22×C3C22×C3×Dic311yescharacteristic
499C3×C4—22no—
500C3×C4—22no—
501C3×C4—62no—
502C3×C4—62no—
503C3×C4—62no—
504C3×C4—62no—
505C3×C4—122no—
506C3×C4—122no—
507C3×C4—182no—
508C3×C4—182no—
509C3×C4—361no—
510C3×C4—361no—
511Dic3—62no—
512Dic3—62no—
513Dic3—121no—
514Dic3—121no—
515Dic3—182no—
516Dic3—182no—
517Dic3—361no—
518Dic3—361no—
519C32—21no—
520C32#495111yescharacteristic, complemented
521C32C3×#38811yescharacteristic, complemented
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23C2×(C3⋊Dic3)⋊C312yes—
529C23C22×(C3⋊D3)⋊C311yescharacteristic
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—92no—
535C2×C4—92no—
536C2×C4—181no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—181no—
540C2×C4—181no—
541C2×C4—181no—
542C2×C4—181no—
543C2×C4—181no—
544C2×C4—181no—
545C2×C4—181no—
546C2×C4C2×(C3⋊Dic3)⋊C312yes—
547C2×C4C2×(C3⋊Dic3)⋊C312yes—
548C2×C3—31no—
549C2×C3—31no—
550C2×C3—31no—
551C2×C3—31no—
552C2×C3—31no—
553C2×C3—31no—
554C2×C3—31no—
555C2×C3—31no—
556C2×C3—31no—
557C2×C3—31no—
558C2×C3—31no—
559C2×C3—31no—
560C2×C3—31no—
561C2×C3—31no—
562C2×C3—42no—
563C2×C3—61no—
564C2×C3—61no—
565C2×C3—61no—
566C2×C3—61no—
567C2×C3—61no—
568C2×C3—61no—
569C2×C3—61no—
570C2×C3—122no—
571C2×C3—122no—
572C2×C3—124no—
573C2×C3C3×#87911yescharacteristic
574C2×C3C3×#88311yescharacteristic
575C2×C3C3×#88411yescharacteristic
576C2×C3C3×#88511yescharacteristic
577C2×C3C3×#92611yescharacteristic
578C2×C3C3×D4×Dic311yescharacteristic
579C2×C3C3×D4×Dic311yescharacteristic
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22#3828⋊C311yescharacteristic
588C22#3828⋊C311yescharacteristic
589C22D4×(C3⋊D3)⋊C311yescharacteristic
590C22D4×(C3⋊D3)⋊C311yescharacteristic
591C22#3830⋊C311yescharacteristic
592C22#3830⋊C311yescharacteristic
593C22C22×(C3⋊Dic3)⋊C311yescharacteristic
594C4—22no—
595C4—22no—
596C4—182no—
597C4—182no—
598C4—361no—
599C4—361no—
600C3—31no—
601C3—31no—
602C3—61no—
603C3C3×#495111yescharacteristic
604C2—42no—
605C2#64088⋊C311yescharacteristic
606C2#64092⋊C311yescharacteristic
607C2#64093⋊C311yescharacteristic
608C2#64094⋊C311yescharacteristic
609C2#64135⋊C311yescharacteristic
610C2D4×(C3⋊Dic3)⋊C311yescharacteristic
611C2D4×(C3⋊Dic3)⋊C311yescharacteristic
subgroupG/H
centerC23C22×(C3⋊D3)⋊C3
commutatorC22×C32C22×C3×C4
Frattini, socleC23×C3C22×C3×D3
FittingC2×C22⋊C4×H(3,𝔽3)C2
prime radicalC24×H(3,𝔽3)C22
cosocleC23×C32C23×C3
hypercenterC2×C22⋊C4(C3⋊D3)⋊C3
hypocenterC32C3×#388
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊((C3⋊Dic3)⋊C3)C2semidirect
5. C2×C4×(C3⋊Dic3)⋊C3C2semidirect
6. #63658⋊C3C2semidirect
7. #63658⋊C3C2semidirect
8. #10592650C3semidirect
17. C22⋊C4×H(3,𝔽3)C4semidirect
27. C2×C4⋊(C3⋊Dic3)C2×C3semidirect
28. C2×C4×C3⋊Dic3C2×C3semidirect
33. #63658C2×C3semidirect
34. #63658C2×C3semidirect
84. C32×C22⋊C4Dic3semidirect
85. C32×C22⋊C4C3×C4semidirect
314. H(3,𝔽3)#388semidirect
441. C22⋊C4(C3⋊Dic3)⋊C3semidirect
520. C32#4951semidirect
521. C32C3×#388semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×H(3,𝔽3)2
C2×#3757⋊C32
C2×C4⋊((C3⋊Dic3)⋊C3)2
C2×C4×(C3⋊Dic3)⋊C32
#63658⋊C32
#105926503
C3×#49513