Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
274 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 7. #5183 | C3 | direct (N × H) |
| 65. C3×Dic3 | Q16 | semidirect |
| 122. Dic3 | C3×Q16 | semidirect |
| 123. C32 | #494 | semidirect |
| 147. C3 | #5183 | direct (N × H) |
| 148. C3 | C3×#494 | 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×#944 | 2 |
| C2×C3×#216 | 2 |
| C2×C3×Dic12 | 2 |
| C3×C8×Dic3 | 2 |
| C3×#494 | 3 |
| #5183 | 3 |