Subgroups — #16813541

Order 3616.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14268631	C₂	1	2	yes	maximal
2	C₂×Q₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₁₁₃	—	2	2	no	—
4	C₂×C₄×C₁₁₃	C₄	1	2	yes	—
5	C₂×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
6	#11744751	—	2	2	no	—
7	C₂²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
8	C₄×C₁₁₃	—	2	2	no	—
9	C₄×C₁₁₃	D₄	1	2	yes	—
10	C₂×C₁₁₃	—	2	1	no	—
11	C₂×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
12	C₁₁₃	#101	1	1	yes	characteristic, complemented, Sylow
13	#101	—	113	1	no	maximal, Sylow
14	C₂×Q₈	D₁₁₃	1	1	yes	characteristic
15	M₁₆	—	113	2	no	—
16	Q₈	—	2	2	no	—
17	C₂×C₄	Dic₁₁₃	1	2	yes	—
18	C₂×C₄	C₂×D₁₁₃	1	1	yes	characteristic
19	C₈	—	226	2	no	—
20	C₂²	C₂×Dic₁₁₃	1	1	yes	characteristic
21	C₄	—	2	2	no	—
22	C₄	C₂²⋊D₁₁₃	1	2	yes	—
23	C₂	—	2	1	no	—
24	C₂	C₂²⋊Dic₁₁₃	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. C₁₁₃	#101	semidirect

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