Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
259 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 259 conjugacy classes of subgroups — too many to draw. Only its 76 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×#869 | C2 | semidirect |
| 4. C4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 5. #63565 | C2 | semidirect |
| 23. #869 | D3 | semidirect |
| 69. C32×C4 | SD16 | semidirect |
| 138. C3×C4 | #214 | semidirect |
| 139. C3×C4 | #215 | semidirect |
| 146. C32 | #461 | semidirect |
| 177. C4 | #3715 | semidirect |
| 181. C3 | #5019 | semidirect |
| 182. C3 | #5083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D12 | 2 |
| C3×#869 | 2 |
| C2×#3715 | 2 |
| C4⋊(C3⋊(C3⋊C8)) | 2 |
| #63565 | 2 |
| #5083 | 3 |
| #5019 | 3 |