Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
298 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 66 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. #64156 | C2 | semidirect |
| 2. C2×C3×#216 | C2 | semidirect |
| 3. C2×C3×#215 | C2 | semidirect |
| 4. #63863 | C2 | semidirect |
| 5. C2×#3717 | C2 | semidirect |
| 7. #63553 | C2 | semidirect |
| 29. C2×#216 | D3 | semidirect |
| 31. C2×#215 | D3 | semidirect |
| 186. C32 | #495 | semidirect |
| 225. C3 | #5168 | semidirect |
| 226. C3 | #5191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64156 | 2 |
| C2×C3×#216 | 2 |
| C2×C3×#215 | 2 |
| #63863 | 2 |
| C2×#3717 | 2 |
| C2×#3714 | 2 |
| #63553 | 2 |
| #5191 | 3 |
| #5168 | 3 |