Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
363 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 363 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 1. C22×C3×Dic6 | C2 | semidirect |
| 3. C2×#3717 | C2 | semidirect |
| 4. C3×#830 | C2 | semidirect |
| 5. #63566 | C2 | semidirect |
| 20. C22×Dic6 | D3 | semidirect |
| 28. #830 | D3 | semidirect |
| 42. C3×Dic6 | D4 | semidirect |
| 74. C22×C32 | SD16 | semidirect |
| 121. Dic6 | #67 | semidirect |
| 148. C22×C3 | #204 | semidirect |
| 149. C22×C3 | #215 | semidirect |
| 172. C32 | #448 | semidirect |
| 207. C22 | #3717 | semidirect |
| 214. C3 | #4738 | semidirect |
| 215. C3 | #5227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic6 | 2 |
| #64139 | 2 |
| C2×#3717 | 2 |
| C3×#830 | 2 |
| #63566 | 2 |
| #5227 | 3 |
| #4738 | 3 |