Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
163 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 163 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 |
|---|---|---|
| 2. C2×C3×Dic6 | C2 | semidirect |
| 3. C3×#214 | C2 | direct (N × H) |
| 4. C2×C3×C3⋊C8 | C2 | semidirect |
| 6. C2×#214 | C3 | direct (N × H) |
| 13. C3×Dic6 | C22 | semidirect |
| 14. C3×C3⋊C8 | C22 | semidirect |
| 19. C2×Dic6 | C2×C3 | semidirect |
| 22. #214 | C2×C3 | direct (N × H) |
| 23. C2×C3⋊C8 | C2×C3 | semidirect |
| 48. Dic6 | C22×C3 | semidirect |
| 50. C3⋊C8 | C22×C3 | semidirect |
| 52. C2×C32 | SD16 | semidirect |
| 75. C32 | C2×SD16 | semidirect |
| 89. C2×C3 | #214 | direct (N × H) |
| 90. C2×C3 | C3×SD16 | semidirect |
| 100. C3 | C2×#214 | direct (N × H) |
| 101. C3 | C2×C3×SD16 | semidirect |
| 103. C2 | C3×#214 | 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×Dic6 | 2 |
| C3×#214 | 2 |
| C2×C3×C3⋊C8 | 2 |
| C2×C3×SD16 | 3 |
| C2×#214 | 3 |