Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
339 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 339 conjugacy classes of subgroups — too many to draw. Only its 78 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×#4894 | C2 | semidirect |
| 2. #10590768 | C2 | semidirect |
| 4. #10589361 | C2 | semidirect |
| 5. C3×#4494 | C2 | semidirect |
| 6. #10589123 | C2 | semidirect |
| 7. #10589105 | C2 | semidirect |
| 21. #63549 | C4 | semidirect |
| 22. #63546 | C4 | semidirect |
| 26. #4894 | D3 | semidirect |
| 35. #4494 | D3 | semidirect |
| 48. C3×Dic12 | C2×C4 | semidirect |
| 49. C3×D24 | C2×C4 | semidirect |
| 55. C3×C3⋊C16 | C2×C4 | semidirect |
| 134. Dic12 | C4×D3 | semidirect |
| 141. D24 | C4×D3 | semidirect |
| 149. C3⋊C16 | C4×D3 | semidirect |
| 258. C32 | AGL(1,ℤ/16) | semidirect |
| 296. C3 | #69310 | semidirect |
| 297. C3 | #70929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4894 | 2 |
| #10590768 | 2 |
| #10590634 | 2 |
| #10589361 | 2 |
| C3×#4494 | 2 |
| #10589123 | 2 |
| #10589105 | 2 |
| #70929 | 3 |
| #69310 | 3 |