Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
261 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 98 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. C3×Q8×Dic3 | C2 | semidirect |
| 4. C32×#103 | C2 | semidirect |
| 6. C3×#815 | C2 | semidirect |
| 7. C3×#807 | C2 | semidirect |
| 9. #4817 | C3 | direct (N × H) |
| 15. C3×#215 | C4 | semidirect |
| 25. Q8×Dic3 | C2×C3 | semidirect |
| 30. C3×#103 | D3 | semidirect |
| 31. C3×#103 | C2×C3 | semidirect |
| 35. #815 | C2×C3 | semidirect |
| 36. #807 | C2×C3 | semidirect |
| 39. C32×Q8 | C2×C4 | semidirect |
| 50. C3×C3⋊C8 | C2×C4 | semidirect |
| 72. #215 | C3×C4 | semidirect |
| 94. #103 | C3×D3 | semidirect |
| 103. C3×Q8 | C4×D3 | semidirect |
| 104. C3×Q8 | C2×C3×C4 | semidirect |
| 130. C3⋊C8 | C2×C3×C4 | semidirect |
| 174. C32 | #440 | semidirect |
| 177. Q8 | C3×C4×D3 | semidirect |
| 212. C3 | #4817 | direct (N × H) |
| 213. C3 | C3×#440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×Dic3 | 2 |
| C2×C3×#215 | 2 |
| C3×#893 | 2 |
| C32×#103 | 2 |
| C3×#821 | 2 |
| C3×#815 | 2 |
| C3×#807 | 2 |
| C3×#440 | 3 |
| #4817 | 3 |