Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
274 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 72 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. #63866 | C2 | semidirect |
| 5. Dic3⋊(C3⋊C8) | C2 | semidirect |
| 6. #63567 | C2 | semidirect |
| 7. #63565 | C2 | semidirect |
| 95. C3×Dic3 | SD16 | semidirect |
| 188. Dic3 | #214 | semidirect |
| 189. C32 | #461 | semidirect |
| 230. C3 | #5019 | semidirect |
| 231. C3 | #5162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3754 | 2 |
| C3×D4×Dic3 | 2 |
| C2×C3×#214 | 2 |
| #63866 | 2 |
| Dic3⋊(C3⋊C8) | 2 |
| #63567 | 2 |
| #63565 | 2 |
| #5162 | 3 |
| #5019 | 3 |