Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
318 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 95 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. #64135 | C2 | semidirect |
| 3. C32×C22⋊C8 | C2 | semidirect |
| 4. #63648 | C2 | semidirect |
| 5. #63648 | C2 | semidirect |
| 6. #63645 | C2 | semidirect |
| 7. #63644 | C2 | semidirect |
| 22. C3×C22⋊C8 | D3 | semidirect |
| 72. C22⋊C8 | C3⋊D3 | semidirect |
| 116. C32 | #482 | semidirect |
| 149. C3 | #4737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64139 | 2 |
| #64135 | 2 |
| C32×C22⋊C8 | 2 |
| #63648 | 2 |
| #63645 | 2 |
| #63644 | 2 |
| #4737 | 3 |