Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
224 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 76 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×#3697 | C2 | semidirect |
| 2. C2×C3×D36 | C2 | semidirect |
| 3. C3×C9×M16 | C2 | semidirect |
| 4. C3×D72 | C2 | semidirect |
| 5. C3×#3664 | C2 | semidirect |
| 7. #63470 | C3 | direct (N × H) |
| 13. C3×D36 | C22 | semidirect |
| 15. C3×Dic18 | C22 | semidirect |
| 16. C3×C8×C9 | C22 | semidirect |
| 22. #3697 | C2×C3 | semidirect |
| 23. C2×D36 | C2×C3 | semidirect |
| 25. C9×M16 | C2×C3 | semidirect |
| 26. D72 | C2×C3 | semidirect |
| 27. #3664 | C2×C3 | semidirect |
| 52. D36 | C22×C3 | semidirect |
| 54. Dic18 | C22×C3 | semidirect |
| 56. C8×C9 | C22×C3 | semidirect |
| 68. C3×M16 | D9 | semidirect |
| 90. C3×C9 | AGL(1,ℤ/8) | semidirect |
| 109. C3×C8 | C2×D9 | semidirect |
| 125. M16 | C3×D9 | semidirect |
| 145. C9 | C3×AGL(1,ℤ/8) | semidirect |
| 154. C8 | C2×C3×D9 | semidirect |
| 173. C3 | #63470 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3697 | 2 |
| C2×C3×D36 | 2 |
| C3×C9×M16 | 2 |
| C3×D72 | 2 |
| C3×#3664 | 2 |
| C3×#908 | 3 |
| #63470 | 3 |