Subgroups — #37558481

Order 23824.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₉₇₈	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅₉₅₆	C₂	1	1	yes	maximal, characteristic
3	C₈×C₁₄₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₄₈₉	—	2	1	no	—
5	C₄×C₁₄₈₉	C₂²	1	1	yes	characteristic
6	Dic₁₄₈₉	—	2	1	no	—
7	C₂×C₁₄₈₉	D₄	1	1	yes	characteristic
8	D₁₄₈₉	—	4	1	no	—
9	C₁₄₈₉	SD₁₆	1	1	yes	characteristic, complemented, Sylow
10	SD₁₆	—	1489	1	no	maximal, Sylow
11	Q₈	—	1489	1	no	—
12	D₄	—	1489	1	no	—
13	C₈	D₁₄₈₉	1	1	yes	characteristic, complemented
14	C₂²	—	2978	1	no	—
15	C₄	—	2978	1	no	—
16	C₄	C₂×D₁₄₈₉	1	1	yes	characteristic
17	C₂	—	5956	1	no	—
18	C₂	D₅₉₅₆	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.