Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
401 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 401 conjugacy classes of subgroups — too many to draw. Only its 94 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. C3×#924 | C2 | semidirect |
| 3. C2×C3×#204 | C2 | semidirect |
| 4. C32×C22⋊C8 | C2 | semidirect |
| 5. C3×#821 | C2 | semidirect |
| 7. #4731 | C3 | direct (N × H) |
| 13. C2×C3×Dic6 | C22 | semidirect |
| 14. C2×C32×C8 | C22 | semidirect |
| 16. C3×C4⋊Dic3 | C22 | semidirect |
| 23. #924 | C2×C3 | semidirect |
| 24. C2×#204 | C2×C3 | semidirect |
| 27. C3×C22⋊C8 | D3 | semidirect |
| 28. C3×C22⋊C8 | C2×C3 | semidirect |
| 29. #821 | C2×C3 | semidirect |
| 58. C2×Dic6 | C22×C3 | semidirect |
| 61. C2×C3×C8 | C2×D3 | semidirect |
| 62. C2×C3×C8 | C22×C3 | semidirect |
| 67. C4⋊Dic3 | C22×C3 | semidirect |
| 72. C22×C32 | SD16 | semidirect |
| 86. C22⋊C8 | C3×D3 | semidirect |
| 134. C2×C8 | C2×C3×D3 | semidirect |
| 150. C22×C3 | #204 | semidirect |
| 151. C22×C3 | C3×SD16 | semidirect |
| 168. C32 | #450 | semidirect |
| 204. C22 | C3×#204 | semidirect |
| 211. C3 | #4731 | direct (N × H) |
| 212. C3 | C3×#450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D12 | 2 |
| C3×#924 | 2 |
| C2×C3×#204 | 2 |
| C32×C22⋊C8 | 2 |
| C3×#821 | 2 |
| C3×#450 | 3 |
| #4731 | 3 |