Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊#19150304 |
| commutator, hypocenter | C3×C72×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C72×C19 | C2×C3 |
| prime radical | C2×C3×C19×#3862 | C2 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×Dic399 | C3 | semidirect |
| 4. C3×C19×#3862 | C4 | semidirect |
| 12. C19×#3862 | Dic3 | semidirect |
| 13. C3×C72×C19 | C3×C4 | semidirect |
| 18. Dic399 | ΓL(1,𝔽8) | semidirect |
| 24. C72×C19 | C3×Dic3 | semidirect |
| 38. C3×#3862 | Dic19 | semidirect |
| 40. C3×C7×C19 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 41. C3×C7×C19 | C4×ΓL(1,𝔽8) | semidirect |
| 59. C3×C72 | C3×Dic19 | semidirect |
| 61. #3862 | Dic57 | semidirect |
| 63. C7×C19 | Dic3×ΓL(1,𝔽8) | semidirect |
| 64. C7×C19 | C3⋊(ΓL(1,𝔽8)⋊C4) | semidirect |
| 80. C3×C19 | #10596872 | semidirect |
| 81. C72 | C3×Dic57 | semidirect |
| 94. C3×C7 | ΓL(1,𝔽8)×Dic19 | semidirect |
| 95. C3×C7 | ΓL(1,𝔽8)⋊Dic19 | semidirect |
| 100. C19 | C3⋊#10596872 | semidirect |
| 109. C7 | C3⋊(ΓL(1,𝔽8)⋊Dic19) | semidirect |
| 110. C7 | ΓL(1,𝔽8)×Dic57 | semidirect |
| 117. C3 | #26013837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C19×#3862 | 2 |
| C7×Dic399 | 3 |
| #26013837 | 3 |
| ΓL(1,𝔽8)×Dic57 | 7 |
| C3⋊(ΓL(1,𝔽8)⋊Dic19) | 7 |
| C3⋊#10596872 | 19 |