Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
465 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 465 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 |
|---|---|---|
| 2. C2×C3×Dic24 | C2 | semidirect |
| 4. C2×#63550 | C2 | semidirect |
| 6. C3×#4503 | C2 | semidirect |
| 7. #10589117 | C2 | semidirect |
| 31. C2×Dic24 | D3 | semidirect |
| 38. #4503 | D3 | semidirect |
| 183. C2×C3⋊D3 | Q32 | semidirect |
| 311. C32 | #2188 | semidirect |
| 356. C3 | #69225 | semidirect |
| 357. C3 | #71502 | 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×Dic24 | 2 |
| #10590857 | 2 |
| C2×#63550 | 2 |
| #10589373 | 2 |
| C3×#4503 | 2 |
| #10589117 | 2 |
| #71502 | 3 |
| #69225 | 3 |