Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
134 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 54 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. C3×#239 | C2 | semidirect |
| 2. C3×#237 | C2 | semidirect |
| 3. C32×SD16 | C2 | semidirect |
| 4. C3×#216 | C2 | semidirect |
| 5. C3×#213 | C2 | semidirect |
| 6. C3×#204 | C2 | semidirect |
| 7. C3×D3×C8 | C2 | semidirect |
| 9. #916 | C3 | direct (N × H) |
| 23. #239 | C2×C3 | semidirect |
| 24. #237 | C2×C3 | semidirect |
| 28. C3×SD16 | D3 | semidirect |
| 29. C3×SD16 | C2×C3 | semidirect |
| 32. #216 | C2×C3 | semidirect |
| 33. #213 | C2×C3 | semidirect |
| 34. #204 | C2×C3 | semidirect |
| 35. D3×C8 | C2×C3 | semidirect |
| 77. SD16 | C3×D3 | semidirect |
| 97. C32 | #135 | semidirect |
| 127. C3 | #916 | direct (N × H) |
| 128. C3 | C3×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#239 | 2 |
| C3×#237 | 2 |
| C32×SD16 | 2 |
| C3×#216 | 2 |
| C3×#213 | 2 |
| C3×#204 | 2 |
| C3×D3×C8 | 2 |
| C3×#135 | 3 |
| #916 | 3 |