Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
631 conjugacy classes of subgroups; only the 266 normal subgroups are shown.
This group has 631 conjugacy classes of subgroups — too many to draw. Only its 266 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. Q8×C3⋊Dic3 | C2 | semidirect |
| 3. C3×Q8×Dic3 | C2 | semidirect |
| 6. #63843 | C2 | semidirect |
| 7. Dic3×Dic6 | C2 | semidirect |
| 11. C3×D3×Q8 | C4 | semidirect |
| 31. Q8×Dic3 | D3 | direct (N × H) |
| 39. C32×Q8 | C2×C4 | semidirect |
| 47. C3×Dic6 | C2×C4 | semidirect |
| 49. D3×Dic3 | Q8 | direct (N × H) |
| 59. D3×Q8 | Dic3 | direct (N × H) |
| 86. C3⋊Dic3 | C2×Q8 | semidirect |
| 89. C3×Dic3 | C2×Q8 | semidirect |
| 101. C3×Q8 | C4×D3 | semidirect |
| 102. C3×Q8 | C2×Dic3 | semidirect |
| 124. Dic6 | C2×Dic3 | semidirect |
| 128. C3×D3 | C4×Q8 | semidirect |
| 164. Dic3 | D3×Q8 | direct (N × H) |
| 166. C32 | C2×C4×Q8 | semidirect |
| 169. Q8 | D3×Dic3 | direct (N × H) |
| 189. D3 | Q8×Dic3 | direct (N × H) |
| 201. C3 | C4×D3×Q8 | semidirect |
| 202. C3 | C2×Q8×Dic3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×Q8 | 2 |
| Q8×C3⋊Dic3 | 2 |
| C3×Q8×Dic3 | 2 |
| D3×C4⋊Dic3 | 2 |
| C4×D3×Dic3 | 2 |
| #63843 | 2 |
| Dic3×Dic6 | 2 |
| C2×Q8×Dic3 | 3 |
| C4×D3×Q8 | 3 |