Subgroups — Q₈×#11745400 #21418616

Order 7456.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11745400	C₂	1	3	yes	maximal
2	C₄×#11745400	C₂	1	3	yes	maximal
3	Q₈×D₂₃₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11745400	C₂²	1	3	yes	—
5	C₂×#11745400	C₂²	1	1	yes	characteristic
6	Dic₄₆₆	C₄	1	3	yes	complemented
7	C₄×D₂₃₃	C₂²	1	3	yes	—
8	Q₈×C₂₃₃	C₄	1	1	yes	characteristic, complemented
9	C₂×D₂₃₃	C₂³	1	1	yes	characteristic
10	#11745400	—	2	3	no	—
11	#11745400	Q₈	1	2	yes	direct product factor
12	C₄×C₂₃₃	C₂×C₄	1	3	yes	—
13	Dic₂₃₃	C₂×C₄	1	3	yes	—
14	C₂×C₂₃₃	C₂²×C₄	1	1	yes	characteristic
15	D₂₃₃	C₂×Q₈	1	1	yes	characteristic
16	D₂₃₃	#41	1	1	yes	characteristic
17	C₂₃₃	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
18	C₄×Q₈	—	233	1	no	maximal, Sylow
19	C₂×Q₈	—	233	1	no	—
20	C₄⋊C₄	—	233	3	no	—
21	C₄²	—	233	3	no	—
22	Q₈	—	233	3	no	—
23	Q₈	#11745400	1	1	yes	characteristic, direct product factor
24	C₂×C₄	—	233	3	no	—
25	C₂×C₄	—	233	1	no	—
26	C₂×C₄	—	233	3	no	—
27	C₂²	—	233	1	no	—
28	C₄	—	466	3	no	—
29	C₄	—	233	2	no	—
30	C₄	—	233	3	no	—
31	C₄	C₂×#11745400	1	3	yes	—
32	C₂	—	233	1	no	—
33	C₂	—	233	1	no	—
34	C₂	C₂²×#11745400	1	1	yes	characteristic

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