Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
147 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 147 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×#237 | C2 | semidirect |
| 2. C3×D3×D4 | C2 | semidirect |
| 3. C32×D8 | C2 | semidirect |
| 4. C3×#214 | C2 | semidirect |
| 5. C3×#213 | C2 | semidirect |
| 6. C3×#204 | C2 | semidirect |
| 7. C3×ΓL(1,𝔽25) | C2 | semidirect |
| 9. #911 | C3 | direct (N × H) |
| 12. C32×D4 | C22 | semidirect |
| 18. C3×Dic6 | C22 | semidirect |
| 19. C32×C8 | C22 | semidirect |
| 20. C3×C3⋊C8 | C22 | semidirect |
| 23. #237 | C2×C3 | semidirect |
| 24. D3×D4 | C2×C3 | semidirect |
| 29. C3×D8 | D3 | semidirect |
| 30. C3×D8 | C2×C3 | semidirect |
| 32. #214 | C2×C3 | semidirect |
| 33. #213 | C2×C3 | semidirect |
| 34. #204 | C2×C3 | semidirect |
| 35. ΓL(1,𝔽25) | C2×C3 | semidirect |
| 54. C3×D4 | C2×D3 | semidirect |
| 56. C3×D4 | C22×C3 | semidirect |
| 64. Dic6 | C22×C3 | semidirect |
| 67. C3×C8 | C2×D3 | semidirect |
| 68. C3×C8 | C22×C3 | semidirect |
| 69. C3⋊C8 | C22×C3 | semidirect |
| 80. D8 | C3×D3 | semidirect |
| 101. C32 | AGL(1,ℤ/8) | semidirect |
| 108. D4 | C2×C3×D3 | semidirect |
| 112. C8 | C2×C3×D3 | semidirect |
| 135. C3 | #911 | direct (N × H) |
| 136. 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 |
|---|---|
| C3×#237 | 2 |
| C3×D3×D4 | 2 |
| C32×D8 | 2 |
| C3×#214 | 2 |
| C3×#213 | 2 |
| C3×#204 | 2 |
| C3×ΓL(1,𝔽25) | 2 |
| C3×AGL(1,ℤ/8) | 3 |
| #911 | 3 |