Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
214 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 214 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 |
| 114. C3⋊C8 | Dic6 | semidirect |
| 115. C3⋊C8 | Dic6 | semidirect |
| 155. C32 | #501 | semidirect |
| 185. C3 | #4856 | semidirect |
| 186. C3 | #4876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64097 | 2 |
| #63872 | 2 |
| C3×#808 | 2 |
| C3×#807 | 2 |
| #63575 | 2 |
| #63573 | 2 |
| #63555 | 2 |
| #4876 | 3 |
| #4856 | 3 |