Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
294 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 72 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×#3744 | C2 | semidirect |
| 2. C2×C3×#204 | C2 | semidirect |
| 3. #63864 | C2 | semidirect |
| 4. #63860 | C2 | semidirect |
| 5. C2×#3719 | C2 | semidirect |
| 7. C3×C8×Dic3 | C2 | semidirect |
| 33. C2×#204 | D3 | semidirect |
| 37. C8×Dic3 | D3 | semidirect |
| 185. C32 | #495 | semidirect |
| 224. C3 | #4696 | semidirect |
| 225. C3 | #5168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3744 | 2 |
| C2×C3×#204 | 2 |
| #63864 | 2 |
| #63860 | 2 |
| C2×#3719 | 2 |
| C2×#3714 | 2 |
| C3×C8×Dic3 | 2 |
| #5168 | 3 |
| #4696 | 3 |