Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
393 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 393 conjugacy classes of subgroups — too many to draw. Only its 92 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×Dic3×D8 | C2 | semidirect |
| 3. #10590763 | C2 | semidirect |
| 4. C3×#4562 | C2 | semidirect |
| 5. #10589142 | C2 | semidirect |
| 6. #10589116 | C2 | semidirect |
| 7. #10589103 | C2 | semidirect |
| 14. #63653 | C4 | semidirect |
| 23. Dic3×D8 | D3 | semidirect |
| 30. #4562 | D3 | semidirect |
| 42. C32×D8 | C2×C4 | semidirect |
| 45. #3745 | C2×C4 | semidirect |
| 52. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 120. C3×D8 | C4×D3 | semidirect |
| 121. C3×D8 | C4×D3 | semidirect |
| 226. D8 | #624 | semidirect |
| 271. C32 | #2177 | semidirect |
| 317. C3 | #69177 | semidirect |
| 318. C3 | #70885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63653 | 2 |
| C3×Dic3×D8 | 2 |
| #10590763 | 2 |
| C3×#4562 | 2 |
| #10589142 | 2 |
| #10589116 | 2 |
| #10589103 | 2 |
| #70885 | 3 |
| #69177 | 3 |