Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
485 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 485 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×#63802 | C2 | semidirect |
| 2. C2×C3×#800 | C2 | semidirect |
| 4. C2×#63547 | C2 | semidirect |
| 5. #10589373 | C2 | semidirect |
| 6. C3×#4503 | C2 | semidirect |
| 7. #10589117 | C2 | semidirect |
| 31. C2×#800 | D3 | semidirect |
| 38. #4503 | D3 | semidirect |
| 56. C3×Dic12 | D4 | semidirect |
| 57. C3×Dic12 | D4 | semidirect |
| 165. Dic12 | D12 | semidirect |
| 166. Dic12 | #67 | semidirect |
| 184. C2×C3⋊D3 | SD32 | semidirect |
| 321. C32 | #2185 | semidirect |
| 371. C3 | #69223 | semidirect |
| 372. C3 | #71483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63802 | 2 |
| C2×C3×#800 | 2 |
| #10590844 | 2 |
| C2×#63547 | 2 |
| #10589373 | 2 |
| C3×#4503 | 2 |
| #10589117 | 2 |
| #71483 | 3 |
| #69223 | 3 |