Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
321 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 321 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 3. C2×C3×Dic12 | C2 | semidirect |
| 5. C3×#816 | C2 | semidirect |
| 7. #4739 | C3 | direct (N × H) |
| 24. C2×Dic12 | C2×C3 | semidirect |
| 29. #816 | C2×C3 | semidirect |
| 70. C22×C32 | Q16 | semidirect |
| 136. C22×C3 | Dic12 | semidirect |
| 137. C22×C3 | C3×Q16 | semidirect |
| 152. C32 | #451 | semidirect |
| 180. C22 | C3×Dic12 | semidirect |
| 188. C3 | #4739 | direct (N × H) |
| 189. C3 | C3×#451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic6 | 2 |
| C3×#924 | 2 |
| C2×C3×Dic12 | 2 |
| C32×C22⋊C8 | 2 |
| C3×#816 | 2 |
| C3×#451 | 3 |
| #4739 | 3 |