Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
714 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 240 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. #64135 | C2 | semidirect |
| 3. C3×#926 | C2 | semidirect |
| 4. D3×#217 | C2 | semidirect |
| 5. #63898 | C2 | semidirect |
| 6. Dic3×D12 | C2 | semidirect |
| 11. C2×C3×D12 | C4 | semidirect |
| 14. C2×D3×Dic3 | C22 | semidirect |
| 16. C4⋊(C3⋊Dic3) | C22 | semidirect |
| 17. C4×C3⋊Dic3 | C22 | semidirect |
| 19. C3×C4⋊Dic3 | C22 | semidirect |
| 20. C3×C4×Dic3 | C22 | semidirect |
| 21. (C2×D3)⋊Dic3 | C22 | semidirect |
| 31. #926 | D3 | semidirect |
| 37. C22×C3×D3 | C2×C4 | semidirect |
| 39. C2×C32×C4 | C2×C4 | semidirect |
| 44. C3×D12 | C2×C4 | semidirect |
| 45. C3×D12 | C2×C4 | semidirect |
| 57. C2×D12 | Dic3 | semidirect |
| 73. C4⋊Dic3 | C2×D3 | semidirect |
| 77. C4×Dic3 | C2×D3 | semidirect |
| 101. C22×D3 | C2×Dic3 | semidirect |
| 109. C2×C3×C4 | C4×D3 | semidirect |
| 110. C2×C3×C4 | C2×Dic3 | semidirect |
| 120. D12 | C2×Dic3 | semidirect |
| 121. D12 | C2×Dic3 | semidirect |
| 166. C32 | #518 | semidirect |
| 176. C2×C4 | D3×Dic3 | semidirect |
| 201. C3 | #5521 | semidirect |
| 202. C3 | #5798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D12 | 2 |
| #64135 | 2 |
| C3×#926 | 2 |
| D3×#217 | 2 |
| #63898 | 2 |
| Dic3×D12 | 2 |
| #5798 | 3 |
| #5521 | 3 |