Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
7584 conjugacy classes of subgroups; only the 372 normal subgroups are shown.
This group has 7584 conjugacy classes of subgroups — too many to draw. Only its 372 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⋊D3×C3⋊(C3⋊D3) |
| commutator, Fitting, socle, cosocle | C2×C35 | C22 |
| hypocenter | C35 | D4 |
| LCS | G ▷ C2×C35 ▷ C35 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3⋊(C3⋊(C3⋊(C3⋊D3))) | C2 | semidirect |
| 2. C2×C32×C3⋊(C3⋊D3) | C2 | semidirect |
| 3. C33×C3⋊Dic3 | C2 | semidirect |
| 12. C2×C3×C3⋊(C3⋊D3) | D3 | semidirect |
| 14. C32×C3⋊Dic3 | D3 | semidirect |
| 16. C35 | D4 | semidirect |
| 34. C2×C3⋊(C3⋊D3) | C3⋊D3 | semidirect |
| 38. C3×C3⋊Dic3 | C3⋊D3 | semidirect |
| 41. C34 | D12 | semidirect |
| 42. C34 | #67 | semidirect |
| 71. C3⋊Dic3 | C3⋊(C3⋊D3) | semidirect |
| 76. C33 | #626 | semidirect |
| 77. C33 | C4⋊(C3⋊D3) | semidirect |
| 78. C33 | #638 | semidirect |
| 106. C32 | #6291 | semidirect |
| 107. C32 | #6292 | semidirect |
| 108. C32 | C4⋊(C3⋊(C3⋊D3)) | semidirect |
| 122. C3 | #10620147 | semidirect |
| 123. C3 | #10620152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊(C3⋊(C3⋊(C3⋊D3))) | 2 |
| C2×C32×C3⋊(C3⋊D3) | 2 |
| C33×C3⋊Dic3 | 2 |
| #10620152 | 3 |
| #10620147 | 3 |