Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
290 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 1. C2×#3755 | C2 | semidirect |
| 2. C3×Q8×Dic3 | C2 | semidirect |
| 3. C2×C3×#215 | C2 | semidirect |
| 5. Dic3⋊(C3⋊C8) | C2 | semidirect |
| 6. #63564 | C2 | semidirect |
| 7. #63562 | C2 | semidirect |
| 25. Q8×Dic3 | D3 | semidirect |
| 29. C2×#215 | D3 | semidirect |
| 41. C32×Q8 | D4 | semidirect |
| 98. C3×Dic3 | SD16 | semidirect |
| 115. C3×Q8 | D12 | semidirect |
| 116. C3×Q8 | #67 | semidirect |
| 198. Dic3 | #215 | semidirect |
| 199. C32 | #460 | semidirect |
| 203. Q8 | #626 | semidirect |
| 245. C3 | #5027 | semidirect |
| 246. C3 | #5163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3755 | 2 |
| C3×Q8×Dic3 | 2 |
| C2×C3×#215 | 2 |
| #63911 | 2 |
| Dic3⋊(C3⋊C8) | 2 |
| #63564 | 2 |
| #63562 | 2 |
| #5163 | 3 |
| #5027 | 3 |