Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
144 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 58 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. C32×#41 | C2 | semidirect |
| 2. C3×#235 | C2 | semidirect |
| 3. C3×#216 | C2 | semidirect |
| 4. C3×#215 | C2 | semidirect |
| 5. C3×#214 | C2 | semidirect |
| 6. C3×#213 | C2 | semidirect |
| 7. C2×C3×C3⋊C8 | C2 | semidirect |
| 9. #950 | C3 | direct (N × H) |
| 23. C3×#41 | D3 | semidirect |
| 24. C3×#41 | C2×C3 | semidirect |
| 25. #235 | C2×C3 | semidirect |
| 31. #216 | C2×C3 | semidirect |
| 32. #215 | C2×C3 | semidirect |
| 33. #214 | C2×C3 | semidirect |
| 34. #213 | C2×C3 | semidirect |
| 35. C2×C3⋊C8 | C2×C3 | semidirect |
| 76. #41 | C3×D3 | semidirect |
| 101. C32 | #135 | semidirect |
| 132. C3 | #950 | direct (N × H) |
| 133. C3 | C3×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#41 | 2 |
| C3×#235 | 2 |
| C3×#216 | 2 |
| C3×#215 | 2 |
| C3×#214 | 2 |
| C3×#213 | 2 |
| C2×C3×C3⋊C8 | 2 |
| C3×#135 | 3 |
| #950 | 3 |