Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
179 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 179 conjugacy classes of subgroups — too many to draw. Only its 66 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×C32×D4 | C2 | semidirect |
| 2. C2×C3×D12 | C2 | semidirect |
| 3. C3×#213 | C2 | direct (N × H) |
| 4. C2×C3×C3⋊C8 | C2 | semidirect |
| 6. C2×#213 | C3 | direct (N × H) |
| 10. C32×D4 | C22 | semidirect |
| 13. C3×D12 | C22 | semidirect |
| 14. C3×C3⋊C8 | C22 | semidirect |
| 17. C2×C3×D4 | D3 | semidirect |
| 18. C2×C3×D4 | C2×C3 | semidirect |
| 19. C2×D12 | C2×C3 | semidirect |
| 22. #213 | C2×C3 | direct (N × H) |
| 23. C2×C3⋊C8 | C2×C3 | semidirect |
| 43. C3×D4 | C2×D3 | semidirect |
| 44. C3×D4 | C22×C3 | semidirect |
| 49. D12 | C22×C3 | semidirect |
| 51. C3⋊C8 | C22×C3 | semidirect |
| 53. C2×C32 | D8 | semidirect |
| 57. C2×D4 | C3×D3 | semidirect |
| 79. C32 | C2×D8 | semidirect |
| 85. D4 | C2×C3×D3 | semidirect |
| 94. C2×C3 | #213 | direct (N × H) |
| 95. C2×C3 | C3×D8 | semidirect |
| 107. C3 | C2×#213 | direct (N × H) |
| 108. C3 | C2×C3×D8 | semidirect |
| 111. C2 | C3×#213 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D4 | 2 |
| C2×C3×D12 | 2 |
| C3×#213 | 2 |
| C2×C3×C3⋊C8 | 2 |
| C2×C3×D8 | 3 |
| C2×#213 | 3 |