Subgroups — #11926384

Order 1216.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	Dic₁₅₂	C₂	1	1	yes	maximal, characteristic
3	C₁₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	Q₁₆×C₁₉	—	2	1	no	—
5	Dic₇₆	—	2	1	no	—
6	C₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	Q₈×C₁₉	—	4	1	no	—
8	Dic₃₈	—	4	1	no	—
9	C₈×C₁₉	D₄	1	1	yes	characteristic
10	C₄×C₁₉	—	8	1	no	—
11	C₄×C₁₉	D₈	1	1	yes	characteristic
12	Dic₁₉	—	8	1	no	—
13	Q₆₄	—	19	1	no	maximal, Sylow
14	C₂×C₁₉	D₁₆	1	1	yes	characteristic
15	Q₃₂	—	19	1	no	—
16	Q₃₂	D₁₉	1	1	yes	characteristic
17	C₃₂	—	19	1	no	—
18	C₁₉	Q₆₄	1	1	yes	characteristic, complemented, Sylow
19	Q₁₆	—	2	1	no	—
20	Q₁₆	—	38	1	no	—
21	C₁₆	C₂×D₁₉	1	1	yes	characteristic
22	Q₈	—	4	1	no	—
23	Q₈	—	76	1	no	—
24	C₈	C₂²⋊D₁₉	1	1	yes	characteristic
25	C₄	—	8	1	no	—
26	C₄	—	152	1	no	—
27	C₄	#64525	1	1	yes	characteristic
28	C₂	#10597283	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₁₉	Q₆₄	semidirect

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