Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
474 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 151 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. C22×C32×C8 | C2 | semidirect |
| 3. #64135 | C2 | semidirect |
| 4. #63648 | C2 | semidirect |
| 5. #63643 | C2 | semidirect |
| 10. #3828 | C4 | semidirect |
| 20. C22×C3×C8 | D3 | semidirect |
| 63. C22×C8 | C3⋊D3 | semidirect |
| 108. C32 | #416 | semidirect |
| 138. C3 | #5113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3828 | 2 |
| C22×C32×C8 | 2 |
| #64135 | 2 |
| #63648 | 2 |
| #63643 | 2 |
| #5113 | 3 |