Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
274 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 112 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. #63575 | C2 | semidirect |
| 5. #63573 | C2 | semidirect |
| 16. C3×#208 | C4 | semidirect |
| 38. C3×C3⋊C8 | C2×C4 | semidirect |
| 63. #208 | Dic3 | semidirect |
| 106. C3⋊C8 | C2×Dic3 | semidirect |
| 150. C32 | #428 | semidirect |
| 184. C3 | #4964 | semidirect |
| 185. C3 | #5121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64135 | 2 |
| C2×C3×C4⋊Dic3 | 2 |
| C2×C3×#208 | 2 |
| #63575 | 2 |
| #63573 | 2 |
| #5121 | 3 |
| #4964 | 3 |