Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
220 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 75 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. C3×C9×M16 | C2 | semidirect |
| 3. C4×C3⋊Dic9 | C2 | semidirect |
| 9. C4⋊(C3⋊D9) | C4 | semidirect |
| 11. #6226 | C4 | semidirect |
| 17. C9×M16 | D3 | semidirect |
| 46. C3×M16 | D9 | semidirect |
| 63. C3×C9 | #104 | semidirect |
| 85. M16 | C3⋊D9 | semidirect |
| 100. C9 | #825 | semidirect |
| 120. C3 | #63384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #88736 | 2 |
| C3×C9×M16 | 2 |
| C4×C3⋊Dic9 | 2 |
| #63652 | 3 |
| #63384 | 3 |