Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
155 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 155 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×Q8 | C2 | semidirect |
| 3. C3×#215 | C2 | direct (N × H) |
| 4. C2×C3×C3⋊C8 | C2 | semidirect |
| 6. C2×#215 | C3 | direct (N × H) |
| 9. C32×Q8 | C22 | semidirect |
| 14. C3×C3⋊C8 | C22 | semidirect |
| 16. C2×C3×Q8 | D3 | semidirect |
| 17. C2×C3×Q8 | C2×C3 | semidirect |
| 22. #215 | C2×C3 | direct (N × H) |
| 23. C2×C3⋊C8 | C2×C3 | semidirect |
| 37. C3×Q8 | C2×D3 | semidirect |
| 38. C3×Q8 | C22×C3 | semidirect |
| 50. C3⋊C8 | C22×C3 | semidirect |
| 51. C2×C32 | SD16 | semidirect |
| 54. C2×Q8 | C3×D3 | semidirect |
| 74. C32 | C2×SD16 | semidirect |
| 77. Q8 | C2×C3×D3 | semidirect |
| 86. C2×C3 | #215 | direct (N × H) |
| 87. C2×C3 | C3×SD16 | semidirect |
| 98. C3 | C2×#215 | direct (N × H) |
| 99. C3 | C2×C3×SD16 | semidirect |
| 101. C2 | C3×#215 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q8 | 2 |
| C2×C3×D12 | 2 |
| C3×#215 | 2 |
| C2×C3×C3⋊C8 | 2 |
| C2×C3×SD16 | 3 |
| C2×#215 | 3 |