Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
234 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 82 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×#888 | C2 | semidirect |
| 3. C32×#107 | C2 | semidirect |
| 5. C3×Dic3⋊C8 | C2 | semidirect |
| 7. C3×#807 | C2 | semidirect |
| 9. #4890 | C3 | direct (N × H) |
| 24. #888 | C2×C3 | semidirect |
| 27. C3×#107 | D3 | semidirect |
| 28. C3×#107 | C2×C3 | semidirect |
| 33. Dic3⋊C8 | C2×C3 | semidirect |
| 35. #807 | C2×C3 | semidirect |
| 44. C3×D12 | Q8 | semidirect |
| 89. #107 | C3×D3 | semidirect |
| 115. D12 | C3×Q8 | semidirect |
| 165. C32 | #474 | semidirect |
| 202. C3 | #4890 | direct (N × H) |
| 203. C3 | C3×#474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#893 | 2 |
| C3×#888 | 2 |
| C32×#107 | 2 |
| C3×#821 | 2 |
| C3×Dic3⋊C8 | 2 |
| C3×#809 | 2 |
| C3×#807 | 2 |
| C3×#474 | 3 |
| #4890 | 3 |