Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
198 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 198 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 |
|---|---|---|
| 44. C3⋊(C3⋊C8) | Q8 | semidirect |
| 45. C3×C3⋊C8 | Q8 | semidirect |
| 111. C3⋊C8 | Dic6 | semidirect |
| 149. C32 | #501 | semidirect |
| 179. C3 | #4856 | semidirect |
| 180. C3 | #5081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#888 | 2 |
| #63869 | 2 |
| #63634 | 2 |
| C3×#808 | 2 |
| #63575 | 2 |
| #63574 | 2 |
| #63554 | 2 |
| #5081 | 3 |
| #4856 | 3 |