Subgroups — C₃×#23778316 #44477271

Order 30396.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×D₁₄₉	C₂	1	1	yes	maximal, characteristic
2	#23778316	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₇×C₁₄₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₇×D₁₄₉	C₂×C₃	1	1	yes	characteristic
5	C₁₇×C₁₄₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×#10597010	—	17	1	no	maximal, Hall
7	C₃×D₁₄₉	D₁₇	1	1	yes	characteristic
8	#10597010	—	17	1	no	Hall
9	C₃×C₁₄₉	Dic₁₇	1	1	yes	characteristic, complemented, Hall
10	D₁₄₉	C₃×D₁₇	1	1	yes	characteristic
11	C₃×Dic₁₇	—	149	1	no	maximal, Hall
12	C₁₄₉	C₃×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₃×C₁₇	—	149	1	no	—
14	Dic₁₇	—	149	1	no	Hall
15	C₃×C₁₇	#10597010	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₇	—	149	1	no	—
17	C₁₇	C₃×#10597010	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	2533	1	no	Hall
19	C₂×C₃	—	149	1	no	—
20	C₄	—	2533	1	no	Sylow
21	C₃	#23778316	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	149	1	no	—

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.