Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
802 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 192 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. C23×C3×Dic3 | C2 | semidirect |
| 3. C2×C3×#217 | C2 | semidirect |
| 4. #63966 | C2 | direct (N × H) |
| 5. C2×Dic3⋊Dic3 | C2 | semidirect |
| 6. C2×#3722 | C2 | semidirect |
| 17. C22×C3×Dic3 | C22 | semidirect |
| 18. C3×#217 | C22 | semidirect |
| 19. Dic3⋊Dic3 | C22 | semidirect |
| 20. #3722 | C22 | semidirect |
| 25. C23×Dic3 | D3 | semidirect |
| 27. C2×#217 | D3 | semidirect |
| 72. C22×Dic3 | C2×D3 | semidirect |
| 74. #217 | C2×D3 | semidirect |
| 138. C2×C32 | #123 | semidirect |
| 188. C32 | C2×#123 | semidirect |
| 210. C2×C3 | #886 | semidirect |
| 211. C2×C3 | #929 | semidirect |
| 232. C3 | C2×#886 | semidirect |
| 233. C3 | C2×#929 | semidirect |
| 236. C2 | #63966 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#638 | 2 |
| C23×C3×Dic3 | 2 |
| C2×C3×#217 | 2 |
| #63966 | 2 |
| C2×Dic3⋊Dic3 | 2 |
| C2×#3722 | 2 |
| C2×#929 | 3 |
| C2×#886 | 3 |