Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
130 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 40 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. D3×Dic6 | C2 | semidirect |
| 3. #3744 | C2 | semidirect |
| 4. C3×Dic12 | C2 | semidirect |
| 5. C3×ΓL(1,𝔽25) | C2 | semidirect |
| 6. #3719 | C2 | semidirect |
| 7. #3717 | C2 | semidirect |
| 30. Dic12 | D3 | semidirect |
| 35. ΓL(1,𝔽25) | D3 | semidirect |
| 96. C32 | #137 | semidirect |
| 124. C3 | #909 | semidirect |
| 125. C3 | #918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3799 | 2 |
| D3×Dic6 | 2 |
| #3744 | 2 |
| C3×Dic12 | 2 |
| C3×ΓL(1,𝔽25) | 2 |
| #3719 | 2 |
| #3717 | 2 |
| #918 | 3 |
| #909 | 3 |