Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
139 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 139 conjugacy classes of subgroups — too many to draw. Only its 44 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×#634 | C2 | semidirect |
| 3. C3×#208 | C2 | semidirect |
| 4. #3719 | C2 | semidirect |
| 5. #3716 | C2 | semidirect |
| 25. #208 | D3 | semidirect |
| 81. C32 | #137 | semidirect |
| 106. C3 | #909 | semidirect |
| 107. C3 | #951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#634 | 2 |
| C3×#235 | 2 |
| C3×#208 | 2 |
| #3719 | 2 |
| #3716 | 2 |
| #951 | 3 |
| #909 | 3 |