Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
342 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 118 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. C2×C32×M16 | C2 | semidirect |
| 3. C3×#926 | C2 | semidirect |
| 4. C3×#825 | C2 | semidirect |
| 6. #5139 | C3 | direct (N × H) |
| 11. C3×#235 | C4 | semidirect |
| 13. C2×C3×D12 | C4 | semidirect |
| 15. C2×C3×Dic6 | C4 | semidirect |
| 17. C32×M16 | C22 | semidirect |
| 21. C3×C4×Dic3 | C22 | semidirect |
| 25. C2×C3×M16 | D3 | semidirect |
| 26. C2×C3×M16 | C2×C3 | semidirect |
| 28. #926 | C2×C3 | semidirect |
| 30. #825 | C2×C3 | semidirect |
| 65. #235 | C3×C4 | semidirect |
| 67. C2×D12 | C3×C4 | semidirect |
| 69. C2×Dic6 | C3×C4 | semidirect |
| 74. C3×M16 | C2×D3 | semidirect |
| 75. C3×M16 | C22×C3 | semidirect |
| 84. C4×Dic3 | C22×C3 | semidirect |
| 98. C2×M16 | C3×D3 | semidirect |
| 162. M16 | C2×C3×D3 | semidirect |
| 199. C32 | #421 | semidirect |
| 246. C3 | #5139 | direct (N × H) |
| 247. C3 | C3×#421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#235 | 2 |
| C2×C32×M16 | 2 |
| C3×#926 | 2 |
| C3×#825 | 2 |
| C3×#421 | 3 |
| #5139 | 3 |