Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1121 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 1121 conjugacy classes of subgroups — too many to draw. Only its 268 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#5521 | C2 | semidirect |
| 3. #10592696 | C2 | semidirect |
| 4. #10591138 | C2 | semidirect |
| 5. #10591085 | C2 | semidirect |
| 6. #10590344 | C2 | semidirect |
| 7. C4×#3713 | C2 | semidirect |
| 16. C3×C4×D12 | C22 | semidirect |
| 17. C2×#3713 | C4 | semidirect |
| 20. #63630 | C22 | semidirect |
| 21. C4×C3⋊(C3⋊C8) | C22 | semidirect |
| 22. #63576 | C22 | semidirect |
| 23. #63574 | C22 | semidirect |
| 24. #63562 | C22 | semidirect |
| 27. #5521 | D3 | semidirect |
| 39. C2×C3×D12 | C2×C4 | semidirect |
| 46. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 54. #3713 | C2×C4 | semidirect |
| 55. #3713 | C2×C4 | semidirect |
| 75. C4×D12 | C2×D3 | semidirect |
| 119. C2×D12 | C4×D3 | semidirect |
| 256. C32 | #2948 | semidirect |
| 294. C3 | #82538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5521 | 2 |
| C22×#3713 | 2 |
| #10592696 | 2 |
| #10591138 | 2 |
| #10591085 | 2 |
| #10590344 | 2 |
| C4×#3713 | 2 |
| #82538 | 3 |