Subgroups — D₆₁₅₂ #27134367

Order 12304.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₀₇₆	C₂	1	2	yes	maximal, complemented
2	C₈×C₇₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₇₆₉	—	2	2	no	—
4	C₄×C₇₆₉	C₂²	1	1	yes	characteristic
5	C₂×C₇₆₉	D₄	1	1	yes	characteristic
6	D₇₆₉	—	4	2	no	—
7	C₇₆₉	D₈	1	1	yes	characteristic, complemented, Sylow
8	D₈	—	769	1	no	maximal, Sylow
9	D₄	—	769	2	no	—
10	C₈	D₇₆₉	1	1	yes	characteristic, complemented
11	C₂²	—	1538	2	no	—
12	C₄	C₂×D₇₆₉	1	1	yes	characteristic
13	C₂	—	3076	2	no	—
14	C₂	D₃₀₇₆	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.