Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
237 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 237 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 14. C3×#216 | C4 | semidirect |
| 62. #216 | Dic3 | semidirect |
| 164. C32 | #441 | semidirect |
| 197. C3 | #5030 | semidirect |
| 198. C3 | #5184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×Dic3 | 2 |
| C2×C3×#216 | 2 |
| Dic3×Dic6 | 2 |
| #63662 | 2 |
| #63573 | 2 |
| #63565 | 2 |
| #63554 | 2 |
| #5184 | 3 |
| #5030 | 3 |