Subgroups — #20297304

Order 7136.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₄₆	C₂	1	2	yes	maximal
2	C₄⋊Dic₂₂₃	C₂	1	4	yes	maximal
3	C₄²×C₂₂₃	C₂	1	1	yes	maximal, characteristic
4	Dic₄₄₆	—	2	4	no	—
5	C₂×Dic₂₂₃	C₂²	1	4	yes	—
6	C₂×C₄×C₂₂₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₂₂₃	C₂²	1	2	yes	—
8	C₂²×C₂₂₃	C₂³	1	1	yes	characteristic
9	C₄×C₂₂₃	D₄	1	2	yes	—
10	C₄×C₂₂₃	Q₈	1	4	yes	complemented
11	Dic₂₂₃	—	2	4	no	—
12	C₂×C₂₂₃	C₂×D₄	1	1	yes	characteristic
13	C₂×C₂₂₃	C₂×Q₈	1	2	yes	—
14	C₂₂₃	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
15	C₄⋊Q₈	—	223	1	no	maximal, Sylow
16	C₂×Q₈	—	223	2	no	—
17	C₄⋊C₄	—	223	4	no	—
18	C₄²	D₂₂₃	1	1	yes	characteristic
19	Q₈	—	446	4	no	—
20	C₂×C₄	—	223	4	no	—
21	C₂×C₄	C₂×D₂₂₃	1	1	yes	characteristic
22	C₂×C₄	C₂×D₂₂₃	1	2	yes	—
23	C₂²	C₂²×D₂₂₃	1	1	yes	characteristic
24	C₄	—	446	4	no	—
25	C₄	D₈₉₂	1	2	yes	—
26	C₄	Dic₄₄₆	1	4	yes	complemented
27	C₂	C₂×D₈₉₂	1	1	yes	characteristic
28	C₂	C₂×Dic₄₄₆	1	2	yes	—

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