Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
190 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 190 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 |
|---|---|---|
| 53. C3×C9 | #101 | semidirect |
| 82. C9 | #824 | semidirect |
| 97. C3 | #63382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6226 | 2 |
| C3×C9×M16 | 2 |
| #88532 | 2 |
| #63651 | 3 |
| #63382 | 3 |