Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
349 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 349 conjugacy classes of subgroups — too many to draw. Only its 86 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×#237 | C2 | semidirect |
| 2. C2×C3×#213 | C2 | semidirect |
| 3. C2×C3×#204 | C2 | semidirect |
| 4. C3×#895 | C2 | semidirect |
| 5. C32×#102 | C2 | semidirect |
| 6. C3×(C2×D3)⋊C8 | C2 | semidirect |
| 7. C3×#810 | C2 | semidirect |
| 9. #4781 | C3 | direct (N × H) |
| 26. C2×#237 | C2×C3 | semidirect |
| 30. C2×#213 | C2×C3 | semidirect |
| 31. C2×#204 | C2×C3 | semidirect |
| 32. #895 | C2×C3 | semidirect |
| 35. C3×#102 | D3 | semidirect |
| 36. C3×#102 | C2×C3 | semidirect |
| 38. (C2×D3)⋊C8 | C2×C3 | semidirect |
| 39. #810 | C2×C3 | semidirect |
| 44. C32×D4 | D4 | semidirect |
| 57. C3×Dic6 | D4 | semidirect |
| 114. #102 | C3×D3 | semidirect |
| 133. C3×D4 | D12 | semidirect |
| 134. C3×D4 | C3×D4 | semidirect |
| 156. Dic6 | C3×D4 | semidirect |
| 220. C32 | #449 | semidirect |
| 231. D4 | C3×D12 | semidirect |
| 273. C3 | #4781 | direct (N × H) |
| 274. C3 | C3×#449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#237 | 2 |
| C2×C3×#213 | 2 |
| C2×C3×#204 | 2 |
| C3×#895 | 2 |
| C32×#102 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| C3×#810 | 2 |
| C3×#449 | 3 |
| #4781 | 3 |