Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
245 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 245 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 |
|---|---|---|
| 2. C2×C3×#216 | C2 | semidirect |
| 3. Dic3×Dic6 | C2 | semidirect |
| 5. #63662 | C2 | semidirect |
| 6. Dic3⋊(C3⋊C8) | C2 | semidirect |
| 27. C2×#216 | D3 | semidirect |
| 181. C32 | #464 | semidirect |
| 220. C3 | #5054 | semidirect |
| 221. C3 | #5185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#947 | 2 |
| C2×C3×#216 | 2 |
| Dic3×Dic6 | 2 |
| C2×#3715 | 2 |
| #63662 | 2 |
| Dic3⋊(C3⋊C8) | 2 |
| #63563 | 2 |
| #5185 | 3 |
| #5054 | 3 |