Subgroups — #27136354

Order 12352.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20259994	C₂	1	2	yes	maximal
2	C₈×#11715871	C₂	1	1	yes	maximal, characteristic
3	#15690567	C₄	1	4	yes	complemented
4	#15690563	C₂²	1	1	yes	characteristic
5	C₄×#11715871	C₄	1	1	yes	characteristic
6	C₈×D₁₉₃	C₄	1	1	yes	characteristic
7	C₂×#11715871	C₈	1	2	yes	—
8	#13095400	C₂×C₄	1	2	yes	—
9	C₄×D₁₉₃	C₂×C₄	1	1	yes	characteristic
10	#13095393	C₈	1	1	yes	characteristic
11	C₈×C₁₉₃	C₈	1	1	yes	characteristic
12	C₂×D₁₉₃	C₂×C₈	1	1	yes	characteristic
13	#11715871	—	2	2	no	—
14	C₄×C₁₉₃	C₂×C₈	1	1	yes	characteristic
15	Dic₁₉₃	C₄²	1	1	yes	characteristic
16	C₂×C₁₉₃	C₄×C₈	1	1	yes	characteristic
17	D₁₉₃	M₃₂	1	2	yes	—
18	C₁₉₃	#346	1	1	yes	characteristic, complemented, Sylow
19	#346	—	193	1	no	maximal, Sylow
20	C₂×C₁₆	—	193	2	no	—
21	C₄×C₈	—	193	1	no	—
22	C₂×C₈	—	193	1	no	—
23	C₂×C₈	—	193	1	no	—
24	C₄²	—	193	1	no	—
25	C₁₆	—	193	4	no	—
26	C₂×C₄	—	193	2	no	—
27	C₂×C₄	—	193	1	no	—
28	C₈	—	193	2	no	—
29	C₈	—	193	1	no	—
30	C₈	#13095402	1	1	yes	characteristic
31	C₂²	—	193	1	no	—
32	C₄	—	386	2	no	—
33	C₄	—	193	1	no	—
34	C₄	C₂×#13095402	1	1	yes	characteristic
35	C₂	—	193	2	no	—
36	C₂	C₄×#13095402	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #15690567	C₄	semidirect
18. C₁₉₃	#346	semidirect

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