Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
390 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 207 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 |
|---|---|---|
| 4. #63642 | C2 | semidirect |
| 5. C8×C3⋊Dic3 | C2 | semidirect |
| 8. C32×M16 | C4 | semidirect |
| 13. C2×C3⋊(C3⋊C8) | C4 | semidirect |
| 32. C3×M16 | Dic3 | semidirect |
| 65. M16 | C3⋊Dic3 | semidirect |
| 80. C32 | #405 | semidirect |
| 100. C3 | #5122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×M16 | 2 |
| #64135 | 2 |
| C22×C3⋊(C3⋊C8) | 2 |
| #63642 | 2 |
| C8×C3⋊Dic3 | 2 |
| #5122 | 3 |