Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
200 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 200 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. (C3⋊D9)⋊Q8 | C2 | semidirect |
| 3. #88523 | C2 | semidirect |
| 4. C9×Dic12 | C2 | semidirect |
| 5. C3×#3664 | C2 | semidirect |
| 6. #88427 | C2 | semidirect |
| 7. #88425 | C2 | semidirect |
| 33. #3664 | D3 | semidirect |
| 83. Dic12 | D9 | semidirect |
| 106. C3×C9 | #137 | semidirect |
| 166. C9 | #915 | semidirect |
| 194. C3 | #63480 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C3⋊D9)⋊Q8 | 2 |
| #88634 | 2 |
| #88523 | 2 |
| C9×Dic12 | 2 |
| C3×#3664 | 2 |
| #88427 | 2 |
| #88425 | 2 |
| #63811 | 3 |
| #63480 | 3 |