Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
218 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 49 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. Q8×C3⋊D9 | C2 | semidirect |
| 3. C9×#216 | C2 | semidirect |
| 4. C3×#3675 | C2 | semidirect |
| 5. #88428 | C2 | semidirect |
| 6. #88415 | C2 | semidirect |
| 7. #88414 | C2 | semidirect |
| 32. #3675 | D3 | semidirect |
| 83. #216 | D9 | semidirect |
| 110. C3×C9 | #137 | semidirect |
| 174. C9 | #915 | semidirect |
| 202. C3 | #63480 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊D9 | 2 |
| #88634 | 2 |
| C9×#216 | 2 |
| C3×#3675 | 2 |
| #88428 | 2 |
| #88415 | 2 |
| #88414 | 2 |
| #63951 | 3 |
| #63480 | 3 |