Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 1. C2×C32×M16 | C2 | semidirect |
| 3. #64133 | C2 | semidirect |
| 4. C2×#3744 | C2 | semidirect |
| 5. #63648 | C2 | semidirect |
| 6. #63645 | C2 | semidirect |
| 7. #63643 | C2 | semidirect |
| 22. C2×C3×M16 | D3 | semidirect |
| 44. C32×C8 | D4 | semidirect |
| 73. C2×M16 | C3⋊D3 | semidirect |
| 94. C3×C8 | #67 | semidirect |
| 126. C32 | #468 | semidirect |
| 142. C8 | #638 | semidirect |
| 161. C3 | #5134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×M16 | 2 |
| #64139 | 2 |
| #64133 | 2 |
| C2×#3744 | 2 |
| #63648 | 2 |
| #63645 | 2 |
| #63643 | 2 |
| #5134 | 3 |