Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
456 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 99 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. #64133 | C2 | semidirect |
| 3. C2×#3746 | C2 | semidirect |
| 4. C2×#3744 | C2 | semidirect |
| 5. C32×C22⋊C8 | C2 | semidirect |
| 6. #63648 | C2 | semidirect |
| 7. #63643 | C2 | semidirect |
| 28. C3×C22⋊C8 | D3 | semidirect |
| 85. C22⋊C8 | C3⋊D3 | semidirect |
| 138. C32 | #452 | semidirect |
| 176. C3 | #4733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3828 | 2 |
| #64133 | 2 |
| C2×#3746 | 2 |
| C2×#3744 | 2 |
| C32×C22⋊C8 | 2 |
| #63648 | 2 |
| #63643 | 2 |
| #4733 | 3 |