Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
198 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 44. C32×C8 | Q8 | semidirect |
| 45. C3×C3⋊C8 | Q8 | semidirect |
| 109. C3×C8 | Dic6 | semidirect |
| 110. C3×C8 | Dic6 | semidirect |
| 111. C3⋊C8 | Dic6 | semidirect |
| 149. C32 | #501 | semidirect |
| 159. C8 | #627 | semidirect |
| 179. C3 | #4702 | semidirect |
| 180. C3 | #4876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63918 | 2 |
| #63869 | 2 |
| #63644 | 2 |
| C3×#818 | 2 |
| C3×#815 | 2 |
| #63575 | 2 |
| #63573 | 2 |
| #4876 | 3 |
| #4702 | 3 |