Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
342 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 342 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. #64149 | C2 | semidirect |
| 2. C2×C3×#214 | C2 | semidirect |
| 3. C2×C3×#213 | C2 | semidirect |
| 4. #63863 | C2 | semidirect |
| 5. C2×#3717 | C2 | semidirect |
| 6. C2×#3714 | C2 | semidirect |
| 7. #63555 | C2 | semidirect |
| 31. C2×#214 | D3 | semidirect |
| 33. C2×#213 | D3 | semidirect |
| 53. C3×C3⋊C8 | D4 | semidirect |
| 54. C3×C3⋊C8 | D4 | semidirect |
| 145. C3⋊C8 | #67 | semidirect |
| 146. C3⋊C8 | #67 | semidirect |
| 195. C32 | #496 | semidirect |
| 239. C3 | #5154 | semidirect |
| 240. C3 | #5176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64149 | 2 |
| C2×C3×#214 | 2 |
| C2×C3×#213 | 2 |
| #63863 | 2 |
| C2×#3717 | 2 |
| C2×#3714 | 2 |
| #63555 | 2 |
| #5176 | 3 |
| #5154 | 3 |