Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
670 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 2. C3×#5076 | C2 | semidirect |
| 3. #10590266 | C2 | semidirect |
| 4. #10589410 | C2 | semidirect |
| 5. #10589081 | C2 | semidirect |
| 14. C3×#869 | C22 | semidirect |
| 15. C4⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 16. C3×C4×C3⋊C8 | C22 | semidirect |
| 23. #5076 | D3 | semidirect |
| 62. #869 | C2×D3 | semidirect |
| 71. C4×C3⋊C8 | C2×D3 | semidirect |
| 85. C3×D12 | SD16 | semidirect |
| 193. D12 | #214 | semidirect |
| 253. C32 | #1629 | semidirect |
| 297. C3 | #71266 | semidirect |
| 298. C3 | #71907 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5717 | 2 |
| C3×#5076 | 2 |
| #10590266 | 2 |
| #10589410 | 2 |
| #10589081 | 2 |
| #71907 | 3 |
| #71266 | 3 |