Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
290 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 66 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×#3756 | C2 | semidirect |
| 2. C3×#947 | C2 | semidirect |
| 3. C2×C3×#215 | C2 | semidirect |
| 4. #63860 | C2 | semidirect |
| 5. C2×#3716 | C2 | semidirect |
| 7. Dic3×C3⋊C8 | C2 | semidirect |
| 25. #947 | D3 | semidirect |
| 29. C2×#215 | D3 | semidirect |
| 184. C32 | #495 | semidirect |
| 222. C3 | #5059 | semidirect |
| 223. C3 | #5168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3756 | 2 |
| C3×#947 | 2 |
| C2×C3×#215 | 2 |
| #63860 | 2 |
| C2×#3716 | 2 |
| C2×#3713 | 2 |
| Dic3×C3⋊C8 | 2 |
| #5168 | 3 |
| #5059 | 3 |