Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
339 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 339 conjugacy classes of subgroups — too many to draw. Only its 88 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×#5152 | C2 | semidirect |
| 3. #10590916 | C2 | semidirect |
| 4. #10589429 | C2 | semidirect |
| 5. #10589136 | C2 | semidirect |
| 6. #10589123 | C2 | semidirect |
| 7. #10589105 | C2 | semidirect |
| 17. C3×#827 | C4 | semidirect |
| 18. C3×#826 | C4 | semidirect |
| 26. #5152 | D3 | semidirect |
| 49. C3×Dic12 | C2×C4 | semidirect |
| 50. C3×D24 | C2×C4 | semidirect |
| 55. C3×C3⋊C16 | C2×C4 | semidirect |
| 74. #827 | Dic3 | semidirect |
| 75. #826 | Dic3 | semidirect |
| 140. Dic12 | C2×Dic3 | semidirect |
| 141. D24 | C2×Dic3 | semidirect |
| 149. C3⋊C16 | C2×Dic3 | semidirect |
| 258. C32 | AGL(1,ℤ/16) | semidirect |
| 296. C3 | #70918 | semidirect |
| 297. C3 | #71515 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5152 | 2 |
| C3×#5147 | 2 |
| #10590916 | 2 |
| #10589429 | 2 |
| #10589136 | 2 |
| #10589123 | 2 |
| #10589105 | 2 |
| #71515 | 3 |
| #70918 | 3 |