Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
288 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 71 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. C22×C3⋊Dic9 | C2 | semidirect |
| 3. C3×#3676 | C2 | semidirect |
| 4. (C2×D3)⋊Dic9 | C2 | semidirect |
| 5. Dic9⋊Dic3 | C2 | semidirect |
| 24. #3676 | D3 | semidirect |
| 89. C3×C9 | #123 | semidirect |
| 145. C9 | #886 | semidirect |
| 173. C3 | #63497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊Dic9 | 2 |
| C2×C9×#67 | 2 |
| C3×#3676 | 2 |
| (C2×D3)⋊Dic9 | 2 |
| Dic9⋊Dic3 | 2 |
| #63962 | 3 |
| #63497 | 3 |