Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
312 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|---|
| 4. #63642 | C2 | semidirect |
| 5. C3×#815 | C2 | semidirect |
| 6. #63555 | C2 | semidirect |
| 7. #63554 | C2 | semidirect |
| 18. C3×D3×C8 | C4 | semidirect |
| 20. D3×C3⋊C8 | C4 | semidirect |
| 34. #815 | D3 | direct (N × H) |
| 44. C32×C8 | C2×C4 | semidirect |
| 45. C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 46. C3×C3⋊C8 | C2×C4 | semidirect |
| 47. C3×C3⋊C8 | C2×C4 | semidirect |
| 73. D3×C8 | Dic3 | semidirect |
| 110. C3×C8 | C4×D3 | semidirect |
| 111. C3×C8 | C2×Dic3 | semidirect |
| 115. C3⋊C8 | C4×D3 | semidirect |
| 116. C3⋊C8 | C2×Dic3 | semidirect |
| 119. C3×D3 | #97 | semidirect |
| 151. C32 | C2×#97 | semidirect |
| 163. C8 | D3×Dic3 | semidirect |
| 171. D3 | #815 | direct (N × H) |
| 181. C3 | D3×#97 | semidirect |
| 182. C3 | C2×#815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×C8 | 2 |
| C4×D3×Dic3 | 2 |
| C2×D3×C3⋊C8 | 2 |
| #63642 | 2 |
| C3×#815 | 2 |
| #63555 | 2 |
| #63554 | 2 |
| C2×#815 | 3 |
| D3×#97 | 3 |