Subgroups — C₄×#10596927 #14558418

Order 2368.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596927	C₂	1	2	yes	maximal
2	C₄×#64436	C₂	1	1	yes	maximal, characteristic
3	C₄²×C₃₇	C₄	1	1	yes	characteristic
4	C₂×#64436	C₄	1	1	yes	characteristic
5	C₂×#64436	C₂²	1	1	yes	characteristic
6	#10596927	C₄	1	4	yes	direct product factor
7	C₂×C₄×C₃₇	C₈	1	2	yes	—
8	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
9	#64436	C₈	1	2	yes	—
10	#64436	C₂×C₄	1	2	yes	—
11	C₂²×C₃₇	C₂×C₈	1	1	yes	characteristic
12	C₄×C₃₇	C₁₆	1	4	yes	complemented
13	C₄×C₃₇	C₄²	1	1	yes	characteristic
14	C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
15	C₂×C₃₇	C₄×C₈	1	1	yes	characteristic
16	C₂×C₃₇	C₂×C₁₆	1	2	yes	—
17	C₄×C₁₆	—	37	1	no	maximal, Sylow
18	C₃₇	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₁₆	—	37	2	no	—
20	C₄×C₈	—	37	1	no	—
21	C₂×C₈	—	37	1	no	—
22	C₂×C₈	—	37	1	no	—
23	C₄²	#3866	1	1	yes	characteristic
24	C₁₆	—	37	4	no	—
25	C₂×C₄	#64438	1	2	yes	—
26	C₂×C₄	C₂×#3866	1	1	yes	characteristic
27	C₈	—	37	2	no	—
28	C₈	—	37	2	no	—
29	C₂²	C₂×#64438	1	1	yes	characteristic
30	C₄	#10596927	1	4	yes	direct product factor
31	C₄	D₃₇⋊C₈	1	1	yes	characteristic
32	C₄	C₄×#3866	1	1	yes	characteristic
33	C₂	C₄×#64438	1	1	yes	characteristic
34	C₂	C₂×#10596927	1	2	yes	—

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.