Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
250 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 72 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. C3×D4×D9 | C2 | semidirect |
| 2. C3×C9×D8 | C2 | semidirect |
| 3. C3×#3673 | C2 | semidirect |
| 4. C3×D72 | C2 | semidirect |
| 5. C3×C8×D9 | C2 | semidirect |
| 7. D8×D9 | C3 | direct (N × H) |
| 9. C3×D4×C9 | C22 | semidirect |
| 11. C3×D36 | C22 | semidirect |
| 13. C3×C8×C9 | C22 | semidirect |
| 14. C3×C9⋊C8 | C22 | semidirect |
| 20. D4×D9 | C2×C3 | semidirect |
| 22. C9×D8 | C2×C3 | semidirect |
| 23. #3673 | C2×C3 | semidirect |
| 24. D72 | C2×C3 | semidirect |
| 25. C8×D9 | C2×C3 | semidirect |
| 43. D4×C9 | C22×C3 | semidirect |
| 45. D36 | C22×C3 | semidirect |
| 48. C8×C9 | C22×C3 | semidirect |
| 49. C9⋊C8 | C22×C3 | semidirect |
| 53. C3×D9 | D8 | direct (N × H) |
| 59. C3×D8 | D9 | direct (N × H) |
| 80. C3×C9 | C2×D8 | semidirect |
| 86. C3×D4 | C2×D9 | semidirect |
| 94. C3×C8 | C2×D9 | semidirect |
| 106. D9 | C3×D8 | direct (N × H) |
| 110. D8 | C3×D9 | direct (N × H) |
| 128. C9 | C2×C3×D8 | semidirect |
| 132. D4 | C2×C3×D9 | semidirect |
| 135. C8 | C2×C3×D9 | semidirect |
| 153. C3 | D8×D9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×D9 | 2 |
| C3×C9×D8 | 2 |
| C3×#3673 | 2 |
| C3×D72 | 2 |
| C3×C8×D9 | 2 |
| C3×D3×D8 | 3 |
| D8×D9 | 3 |