Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
9000 conjugacy classes of subgroups; only the 1801 normal subgroups are shown.
This group has 9000 conjugacy classes of subgroups — too many to draw. Only its 1801 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×C3⋊D3 |
| commutator, cosocle | C22×C32 | C25 |
| Frattini | C22 | C24×C3⋊D3 |
| Fitting | C22×C32×C42 | C2 |
| socle | C24×C32 | C23 |
| hypercenter | C22×C42 | C3⋊D3 |
| hypocenter | C32 | C22×#127 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C24 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C4⋊(C3⋊D3) | C2 | semidirect |
| 2. C22×C32×C42 | C2 | semidirect |
| 3. C2×#64083 | C2 | direct (N × H) |
| 8. C22×C4⋊(C3⋊D3) | C22 | semidirect |
| 9. C2×C32×C42 | C22 | semidirect |
| 10. #64083 | C22 | direct (N × H) |
| 12. C22×C3×C42 | D3 | semidirect |
| 17. C22×C32×C4 | D4 | semidirect |
| 20. C2×C4⋊(C3⋊D3) | C23 | semidirect |
| 21. C32×C42 | C23 | semidirect |
| 27. C2×C3×C42 | C2×D3 | semidirect |
| 34. C2×C32×C4 | C2×D4 | semidirect |
| 39. C22×C42 | C3⋊D3 | semidirect |
| 43. C22×C3×C4 | D12 | semidirect |
| 47. C3×C42 | C22×D3 | semidirect |
| 48. C22×C32 | #127 | semidirect |
| 53. C32×C4 | C22×D4 | semidirect |
| 59. C2×C42 | C2×C3⋊D3 | semidirect |
| 65. C2×C3×C4 | C2×D12 | semidirect |
| 68. C2×C32 | C2×#127 | semidirect |
| 76. C22×C4 | C4⋊(C3⋊D3) | semidirect |
| 78. C42 | C22×C3⋊D3 | semidirect |
| 79. C22×C3 | #874 | semidirect |
| 84. C3×C4 | C22×D12 | semidirect |
| 85. C32 | C22×#127 | semidirect |
| 92. C2×C4 | C2×C4⋊(C3⋊D3) | semidirect |
| 94. C2×C3 | C2×#874 | semidirect |
| 99. C22 | #64083 | direct (N × H) |
| 102. C4 | C22×C4⋊(C3⋊D3) | semidirect |
| 103. C3 | C22×#874 | semidirect |
| 105. C2 | C2×#64083 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊(C3⋊D3) | 2 |
| C22×C32×C42 | 2 |
| C2×#64083 | 2 |
| C22×#874 | 3 |