Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
254 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
| 3. C3×Q8×Dic3 | C2 | semidirect |
| 5. C3×#835 | C2 | semidirect |
| 7. C3×Dic3⋊C8 | C2 | semidirect |
| 9. #5185 | C3 | direct (N × H) |
| 24. C2×C3×Q16 | D3 | semidirect |
| 25. C2×C3×Q16 | C2×C3 | semidirect |
| 30. Q8×Dic3 | C2×C3 | semidirect |
| 35. #835 | C2×C3 | semidirect |
| 37. Dic3⋊C8 | C2×C3 | semidirect |
| 95. C2×Q16 | C3×D3 | semidirect |
| 184. C32 | #464 | semidirect |
| 223. C3 | #5185 | direct (N × H) |
| 224. C3 | C3×#464 | 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 |
| C3×Q8×Dic3 | 2 |
| C2×C3×#215 | 2 |
| C3×#835 | 2 |
| C3×#821 | 2 |
| C3×Dic3⋊C8 | 2 |
| C3×#464 | 3 |
| #5185 | 3 |