Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
714 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 254 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. C22×C3×Dic6 | C2 | semidirect |
| 3. C2×C32×C42 | C2 | semidirect |
| 4. C2×C3×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C3×#875 | C2 | direct (N × H) |
| 7. C2×#875 | C3 | direct (N × H) |
| 15. C2×C3×Dic6 | C22 | semidirect |
| 16. C32×C42 | C22 | semidirect |
| 17. C3×(C2×D3)⋊C4 | C22 | semidirect |
| 21. C22×Dic6 | C2×C3 | semidirect |
| 25. C2×C3×C42 | D3 | semidirect |
| 26. C2×C3×C42 | C2×C3 | semidirect |
| 27. C2×(C2×D3)⋊C4 | C2×C3 | semidirect |
| 28. #875 | C2×C3 | direct (N × H) |
| 59. C2×Dic6 | C22×C3 | semidirect |
| 62. C3×C42 | C2×D3 | semidirect |
| 63. C3×C42 | C22×C3 | semidirect |
| 64. (C2×D3)⋊C4 | C22×C3 | semidirect |
| 78. C2×C42 | C3×D3 | semidirect |
| 108. C2×C32 | #124 | semidirect |
| 121. C42 | C2×C3×D3 | semidirect |
| 145. C32 | C2×#124 | semidirect |
| 162. C2×C3 | #875 | direct (N × H) |
| 163. C2×C3 | C3×#124 | semidirect |
| 179. C3 | C2×#875 | direct (N × H) |
| 180. C3 | C2×C3×#124 | semidirect |
| 182. C2 | C3×#875 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D12 | 2 |
| C22×C3×Dic6 | 2 |
| C2×C32×C42 | 2 |
| C2×C3×(C2×D3)⋊C4 | 2 |
| C3×#875 | 2 |
| C2×C3×#124 | 3 |
| C2×#875 | 3 |