Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
242 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 88 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×C3×Q8×C9 | C2 | semidirect |
| 3. C3×#3675 | C2 | direct (N × H) |
| 4. C2×C3×C9⋊C8 | C2 | semidirect |
| 6. C2×#3675 | C3 | direct (N × H) |
| 9. C3×Q8×C9 | C22 | semidirect |
| 14. C3×C9⋊C8 | C22 | semidirect |
| 20. C2×Q8×C9 | C2×C3 | semidirect |
| 22. #3675 | C2×C3 | direct (N × H) |
| 23. C2×C9⋊C8 | C2×C3 | semidirect |
| 44. Q8×C9 | C22×C3 | semidirect |
| 51. C9⋊C8 | C22×C3 | semidirect |
| 52. C2×C3×C9 | SD16 | semidirect |
| 56. C2×C3×Q8 | D9 | semidirect |
| 81. C3×C9 | C2×SD16 | semidirect |
| 88. C3×Q8 | C2×D9 | semidirect |
| 107. C2×C9 | C3×SD16 | semidirect |
| 110. C2×Q8 | C3×D9 | semidirect |
| 132. C9 | C2×C3×SD16 | semidirect |
| 135. Q8 | C2×C3×D9 | semidirect |
| 144. C2×C3 | #3675 | direct (N × H) |
| 156. C3 | C2×#3675 | direct (N × H) |
| 159. C2 | C3×#3675 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×C9 | 2 |
| C2×C3×D36 | 2 |
| C3×#3675 | 2 |
| C2×C3×C9⋊C8 | 2 |
| C2×C3×#215 | 3 |
| C2×#3675 | 3 |