Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
200 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 200 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 |
|---|---|---|
| 2. C2×C3×Dic18 | C2 | semidirect |
| 3. C3×C9×M16 | C2 | semidirect |
| 4. C3×#3664 | C2 | semidirect |
| 5. C3×Dic36 | C2 | semidirect |
| 7. #63471 | C3 | direct (N × H) |
| 23. C2×Dic18 | C2×C3 | semidirect |
| 25. C9×M16 | C2×C3 | semidirect |
| 26. #3664 | C2×C3 | semidirect |
| 27. Dic36 | C2×C3 | semidirect |
| 66. C3×M16 | D9 | semidirect |
| 86. C3×C9 | #137 | semidirect |
| 119. M16 | C3×D9 | semidirect |
| 137. C9 | C3×#137 | semidirect |
| 162. C3 | #63471 | 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×Dic18 | 2 |
| C3×C9×M16 | 2 |
| C3×#3664 | 2 |
| C3×Dic36 | 2 |
| C3×#909 | 3 |
| #63471 | 3 |