Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
220 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 59 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×C9×Dic6 | C2 | semidirect |
| 3. C3×#3667 | C2 | semidirect |
| 4. #88428 | C2 | semidirect |
| 5. #88426 | C2 | semidirect |
| 27. #3667 | D3 | semidirect |
| 66. C2×Dic6 | D9 | semidirect |
| 91. C3×C9 | #137 | semidirect |
| 148. C9 | #909 | semidirect |
| 174. C3 | #63505 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #88736 | 2 |
| C2×C9×Dic6 | 2 |
| C3×#3667 | 2 |
| #88428 | 2 |
| #88426 | 2 |
| #63833 | 3 |
| #63505 | 3 |