Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
249 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 249 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 3. Dic3×Dic6 | C2 | semidirect |
| 4. C2×#3718 | C2 | semidirect |
| 6. Dic3⋊(C3⋊C8) | C2 | semidirect |
| 7. #63566 | C2 | semidirect |
| 183. C32 | #464 | semidirect |
| 223. C3 | #5054 | semidirect |
| 224. C3 | #5166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#936 | 2 |
| C2×C3×#214 | 2 |
| Dic3×Dic6 | 2 |
| C2×#3718 | 2 |
| #63659 | 2 |
| Dic3⋊(C3⋊C8) | 2 |
| #63566 | 2 |
| #5166 | 3 |
| #5054 | 3 |