Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
450 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 139 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. C2×C32×M16 | C2 | semidirect |
| 3. C2×#3748 | C2 | semidirect |
| 4. #63651 | C2 | semidirect |
| 5. #63650 | C2 | semidirect |
| 23. C2×C3×M16 | D3 | semidirect |
| 75. C2×M16 | C3⋊D3 | semidirect |
| 128. C32 | #413 | semidirect |
| 164. C3 | #5132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3828 | 2 |
| C2×C32×M16 | 2 |
| C2×#3748 | 2 |
| #63651 | 2 |
| #63650 | 2 |
| #5132 | 3 |