Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
308 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 68 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×C3×D24 | C2 | semidirect |
| 2. C2×C3×#204 | C2 | semidirect |
| 3. #63914 | C2 | semidirect |
| 4. #63863 | C2 | semidirect |
| 5. C2×#3715 | C2 | semidirect |
| 6. C2×#3713 | C2 | semidirect |
| 7. #63642 | C2 | semidirect |
| 33. C2×D24 | D3 | semidirect |
| 34. C2×#204 | D3 | semidirect |
| 53. C32×C8 | D4 | semidirect |
| 54. C3⋊(C3⋊C8) | D4 | semidirect |
| 136. C3×C8 | #67 | semidirect |
| 137. C3×C8 | #67 | semidirect |
| 185. C32 | #496 | semidirect |
| 202. C8 | #625 | semidirect |
| 227. C3 | #5154 | semidirect |
| 228. C3 | #5176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D24 | 2 |
| C2×C3×#204 | 2 |
| #63914 | 2 |
| #63863 | 2 |
| C2×#3715 | 2 |
| C2×#3713 | 2 |
| #63642 | 2 |
| #5176 | 3 |
| #5154 | 3 |