Subgroups — #13096146

Order 1568.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#11716063	C₂	1	1	yes	maximal, characteristic
3	C₇⋊(C₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇²×Q₈	—	2	1	no	—
5	C₄⋊(C₇⋊D₇)	—	2	1	no	—
6	C₇²×C₈	C₂²	1	1	yes	characteristic
7	#6402	—	7	8	no	maximal
8	C₂×C₇⋊D₇	—	4	1	no	—
9	C₄×C₇²	—	4	1	no	—
10	C₄×C₇²	D₄	1	1	yes	characteristic
11	C₇×Q₁₆	D₇	1	8	yes	complemented
12	D₅₆	—	7	8	no	—
13	C₇⋊C₁₆	—	7	8	no	—
14	C₂×C₇²	D₈	1	1	yes	characteristic
15	C₇⋊D₇	—	8	1	no	—
16	C₇×Q₈	—	2	8	no	—
17	D₂₈	—	14	8	no	—
18	C₇×C₈	C₂×D₇	1	8	yes	—
19	C₇²	SD₃₂	1	1	yes	characteristic, complemented, Sylow
20	SD₃₂	—	49	1	no	Sylow
21	C₂×D₇	—	28	8	no	—
22	C₄×C₇	—	4	8	no	—
23	C₄×C₇	C₂²⋊D₇	1	8	yes	—
24	Q₁₆	C₇⋊D₇	1	1	yes	characteristic, complemented
25	D₈	—	49	1	no	—
26	C₁₆	—	49	1	no	—
27	C₂×C₇	#1141	1	8	yes	—
28	D₇	—	56	8	no	—
29	Q₈	—	2	1	no	—
30	D₄	—	98	1	no	—
31	C₈	C₂×C₇⋊D₇	1	1	yes	characteristic
32	C₇	#6402	1	8	yes	complemented
33	C₂²	—	196	1	no	—
34	C₄	—	4	1	no	—
35	C₄	C₂²⋊(C₇⋊D₇)	1	1	yes	characteristic
36	C₂	—	392	1	no	—
37	C₂	#11716071	1	1	yes	characteristic

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

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