Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
290 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 86 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×Q16 | C2 | semidirect |
| 2. C3×#947 | C2 | semidirect |
| 3. C2×C3×#215 | C2 | semidirect |
| 5. C3×C8×Dic3 | C2 | semidirect |
| 7. #5191 | C3 | direct (N × H) |
| 18. C2×C3×Q16 | D3 | semidirect |
| 19. C2×C3×Q16 | C2×C3 | semidirect |
| 23. #947 | C2×C3 | semidirect |
| 24. C2×#215 | C2×C3 | semidirect |
| 27. C8×Dic3 | C2×C3 | semidirect |
| 67. C2×Q16 | C3×D3 | semidirect |
| 127. C32 | #495 | semidirect |
| 154. C3 | #5191 | direct (N × H) |
| 155. C3 | C3×#495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q16 | 2 |
| C3×#947 | 2 |
| C2×C3×#215 | 2 |
| C2×C3×D24 | 2 |
| C3×C8×Dic3 | 2 |
| C3×#495 | 3 |
| #5191 | 3 |