Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
263 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 263 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 2. C3×#869 | C2 | semidirect |
| 3. C3×C4⋊(C3⋊C8) | C2 | semidirect |
| 4. #63575 | C2 | semidirect |
| 21. #869 | D3 | semidirect |
| 27. C4⋊(C3⋊C8) | D3 | semidirect |
| 34. C4⋊(C3⋊D3) | Q8 | semidirect |
| 150. C32 | #474 | semidirect |
| 185. C3 | #4846 | semidirect |
| 186. C3 | #5087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C3⋊D3) | 2 |
| C3×#869 | 2 |
| C3×C4⋊(C3⋊C8) | 2 |
| #63575 | 2 |
| #63564 | 2 |
| #5087 | 3 |
| #4846 | 3 |