Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
300 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 101 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×#6226 | C2 | semidirect |
| 3. C3×C9×M16 | C2 | semidirect |
| 4. #88524 | C2 | semidirect |
| 5. #88521 | C2 | semidirect |
| 24. C9×M16 | D3 | semidirect |
| 60. C3×M16 | D9 | semidirect |
| 79. C3×C9 | #137 | semidirect |
| 108. M16 | C3⋊D9 | semidirect |
| 122. C9 | #909 | semidirect |
| 144. C3 | #63471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #88736 | 2 |
| C2×#6226 | 2 |
| C3×C9×M16 | 2 |
| #88524 | 2 |
| #88521 | 2 |
| #64118 | 3 |
| #63471 | 3 |