Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
300 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 83 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. Q8×C3⋊D9 | C2 | semidirect |
| 3. C3×C9×Q16 | C2 | semidirect |
| 4. #88548 | C2 | semidirect |
| 5. #88547 | C2 | semidirect |
| 6. #88524 | C2 | semidirect |
| 7. #88523 | C2 | semidirect |
| 30. C9×Q16 | D3 | semidirect |
| 73. C3×Q16 | D9 | semidirect |
| 98. C3×C9 | #137 | semidirect |
| 130. Q16 | C3⋊D9 | semidirect |
| 149. C9 | #918 | semidirect |
| 174. C3 | #63480 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #88746 | 2 |
| Q8×C3⋊D9 | 2 |
| C3×C9×Q16 | 2 |
| #88548 | 2 |
| #88547 | 2 |
| #88524 | 2 |
| #88523 | 2 |
| #64127 | 3 |
| #63480 | 3 |