Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
156 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 156 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. C2×C3×D12 | C2 | semidirect |
| 3. C3×#215 | C2 | semidirect |
| 4. C3×#213 | C2 | semidirect |
| 5. C3×#208 | C2 | semidirect |
| 7. #949 | C3 | direct (N × H) |
| 9. C32×Q8 | C22 | semidirect |
| 11. C32×D4 | C22 | semidirect |
| 16. C3×C3⋊C8 | C22 | semidirect |
| 18. C3×#41 | D3 | semidirect |
| 19. C3×#41 | C2×C3 | semidirect |
| 21. C2×D12 | C2×C3 | semidirect |
| 25. #215 | C2×C3 | semidirect |
| 26. #213 | C2×C3 | semidirect |
| 27. #208 | C2×C3 | semidirect |
| 39. C3×Q8 | C2×D3 | semidirect |
| 40. C3×Q8 | C22×C3 | semidirect |
| 47. C3×D4 | C2×D3 | semidirect |
| 48. C3×D4 | C22×C3 | semidirect |
| 58. C3⋊C8 | C22×C3 | semidirect |
| 63. #41 | C3×D3 | semidirect |
| 87. C32 | AGL(1,ℤ/8) | semidirect |
| 89. Q8 | C2×C3×D3 | semidirect |
| 93. D4 | C2×C3×D3 | semidirect |
| 116. C3 | #949 | direct (N × H) |
| 117. C3 | C3×AGL(1,ℤ/8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#41 | 2 |
| C2×C3×D12 | 2 |
| C3×#215 | 2 |
| C3×#213 | 2 |
| C3×#208 | 2 |
| C3×AGL(1,ℤ/8) | 3 |
| #949 | 3 |