Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
440 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 82 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. #89019 | C2 | semidirect |
| 3. #88850 | C2 | semidirect |
| 4. C3×#3746 | C2 | semidirect |
| 5. C32×#204 | C2 | semidirect |
| 6. #88798 | C2 | semidirect |
| 7. #88792 | C2 | semidirect |
| 28. #3746 | D3 | semidirect |
| 33. C3×#204 | D3 | semidirect |
| 84. #204 | C3⋊D3 | semidirect |
| 106. C33 | #137 | semidirect |
| 165. C32 | #915 | semidirect |
| 166. C32 | #918 | semidirect |
| 194. C3 | #63811 | semidirect |
| 195. C3 | #64124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #89019 | 2 |
| #89015 | 2 |
| #88850 | 2 |
| C3×#3746 | 2 |
| C32×#204 | 2 |
| #88798 | 2 |
| #88792 | 2 |
| #64124 | 3 |
| #63811 | 3 |