Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
268 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 65 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×D3×Dic9 | C2 | semidirect |
| 3. #88536 | C2 | semidirect |
| 4. C9×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C3×C4⋊Dic9 | C2 | semidirect |
| 6. #88445 | C2 | semidirect |
| 7. Dic3⋊Dic9 | C2 | semidirect |
| 33. C4⋊Dic9 | D3 | semidirect |
| 85. (C2×D3)⋊C4 | D9 | semidirect |
| 120. C3×C9 | #123 | semidirect |
| 195. C9 | #894 | semidirect |
| 232. C3 | #63448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6195 | 2 |
| C2×D3×Dic9 | 2 |
| #88536 | 2 |
| C9×(C2×D3)⋊C4 | 2 |
| C3×C4⋊Dic9 | 2 |
| #88445 | 2 |
| Dic3⋊Dic9 | 2 |
| #63890 | 3 |
| #63448 | 3 |