Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
358 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 126 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. C2×C3×C4⋊Dic3 | C2 | semidirect |
| 4. C3×#821 | C2 | semidirect |
| 5. C3×#816 | C2 | semidirect |
| 7. #5133 | C3 | direct (N × H) |
| 12. C3×#235 | C4 | semidirect |
| 23. C2×C3×M16 | D3 | semidirect |
| 24. C2×C3×M16 | C2×C3 | semidirect |
| 26. C2×C4⋊Dic3 | C2×C3 | semidirect |
| 29. #821 | C2×C3 | semidirect |
| 30. #816 | C2×C3 | semidirect |
| 42. C3×D12 | C2×C4 | semidirect |
| 45. C3×Dic6 | C2×C4 | semidirect |
| 61. #235 | C3×C4 | semidirect |
| 88. C2×M16 | C3×D3 | semidirect |
| 123. D12 | C2×C3×C4 | semidirect |
| 126. Dic6 | C2×C3×C4 | semidirect |
| 178. C32 | #417 | semidirect |
| 222. C3 | #5133 | direct (N × H) |
| 223. C3 | C3×#417 | 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 |
| C2×C3×C4⋊Dic3 | 2 |
| C3×#821 | 2 |
| C3×#816 | 2 |
| C3×#417 | 3 |
| #5133 | 3 |