Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
174 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 42 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 |
|---|---|---|
| 17. C9×A4 | Q8 | semidirect |
| 46. C22×C9 | Dic6 | semidirect |
| 47. C22⋊C9 | Dic6 | semidirect |
| 78. A4 | Dic18 | semidirect |
| 87. C9 | A4⋊Q8 | semidirect |
| 101. C22 | #6226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C9×A4 | 2 |
| C9⋊SL(2,ℤ/4) | 2 |
| #64259 | 3 |
| (C22⋊C9)⋊Q8 | 3 |
| #63486 | 3 |
| #6226 | 4 |