Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
288 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 61 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×(C3⋊D9)⋊C4 | C2 | semidirect |
| 3. C9×Dic3⋊C4 | C2 | semidirect |
| 4. C3×Dic9⋊C4 | C2 | semidirect |
| 5. #88445 | C2 | semidirect |
| 6. #88445 | C2 | semidirect |
| 7. #88445 | C2 | semidirect |
| 33. Dic9⋊C4 | D3 | semidirect |
| 89. Dic3⋊C4 | D9 | semidirect |
| 123. C3×C9 | #123 | semidirect |
| 202. C9 | #894 | semidirect |
| 240. C3 | #63456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊D9) | 2 |
| C2×(C3⋊D9)⋊C4 | 2 |
| C9×Dic3⋊C4 | 2 |
| C3×Dic9⋊C4 | 2 |
| #88445 | 2 |
| #63897 | 3 |
| #63456 | 3 |