Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
650 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 125 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. C23×C3⋊D9 | C2 | semidirect |
| 2. C2×C3×D4×C9 | C2 | semidirect |
| 3. C2×#6233 | C2 | semidirect |
| 4. #88551 | C2 | semidirect |
| 5. #88536 | C2 | semidirect |
| 9. C23×C3×C9 | C22 | semidirect |
| 14. C2×C3×C4×C9 | C22 | semidirect |
| 16. C2×C3⋊Dic9 | C22 | semidirect |
| 23. C2×D4×C9 | D3 | semidirect |
| 30. C22×C3×C9 | D4 | semidirect |
| 35. C2×C3⋊D9 | D4 | semidirect |
| 50. C23×C9 | C2×D3 | semidirect |
| 55. C2×C4×C9 | C2×D3 | semidirect |
| 65. C2×C3×D4 | D9 | semidirect |
| 87. C22×C9 | #67 | semidirect |
| 96. C3×C9 | #120 | semidirect |
| 98. C23×C3 | C2×D9 | semidirect |
| 109. C2×C3×C4 | C2×D9 | semidirect |
| 127. C2×D4 | C3⋊D9 | semidirect |
| 136. C22×C3 | #611 | semidirect |
| 153. C9 | #937 | semidirect |
| 158. C23 | C2×C3⋊D9 | semidirect |
| 162. C2×C4 | C2×C3⋊D9 | semidirect |
| 180. C22 | #6233 | semidirect |
| 184. C3 | #63499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3⋊D9 | 2 |
| C2×C3×D4×C9 | 2 |
| C2×#6233 | 2 |
| #88551 | 2 |
| #88536 | 2 |
| #64146 | 3 |
| #63499 | 3 |