Subgroups — #34085307

Order 19424.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₂₁₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₀₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×C₆₀₇	C₂	1	1	yes	maximal, characteristic
4	Dic₁₂₁₄	—	2	1	no	—
5	Dic₁₂₁₄	C₄	1	2	yes	complemented
6	C₂×Dic₆₀₇	—	2	1	no	—
7	C₆₀₇⋊C₈	—	2	1	no	—
8	C₂×C₄×C₆₀₇	—	2	1	no	—
9	C₂×C₄×C₆₀₇	C₂²	1	1	yes	characteristic
10	C₂²×C₆₀₇	D₄	1	1	yes	characteristic
11	C₄×C₆₀₇	—	4	1	no	—
12	C₄×C₆₀₇	C₂×C₄	1	1	yes	characteristic
13	C₄×C₆₀₇	D₄	1	1	yes	characteristic
14	Dic₆₀₇	—	2	2	no	—
15	C₂×C₆₀₇	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×C₆₀₇	SD₁₆	1	1	yes	characteristic
17	C₂×C₆₀₇	Q₁₆	1	1	yes	characteristic
18	C₆₀₇	#103	1	1	yes	characteristic, complemented, Sylow
19	#103	—	607	1	no	maximal, Sylow
20	C₂×Q₈	—	607	1	no	—
21	C₂×C₈	—	607	1	no	—
22	C₄⋊C₄	D₆₀₇	1	1	yes	characteristic
23	Q₈	—	607	2	no	—
24	Q₈	—	1214	1	no	—
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	—	1214	1	no	—
27	C₂×C₄	C₂×D₆₀₇	1	1	yes	characteristic
28	C₈	—	1214	1	no	—
29	C₂²	C₂²⋊D₆₀₇	1	1	yes	characteristic
30	C₄	—	4	1	no	—
31	C₄	—	1214	2	no	—
32	C₄	C₄×D₆₀₇	1	1	yes	characteristic
33	C₄	D₂₄₂₈	1	1	yes	characteristic
34	C₂	(C₂×D₆₀₇)⋊C₄	1	1	yes	characteristic
35	C₂	#23753455	1	1	yes	characteristic
36	C₂	#23753457	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. Dic₁₂₁₄	C₄	semidirect
18. C₆₀₇	#103	semidirect

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