Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
310 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 310 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 |
|---|---|---|
| 1. #88746 | C2 | semidirect |
| 2. C3×C9×Q16 | C2 | semidirect |
| 3. #88548 | C2 | semidirect |
| 4. #88525 | C2 | semidirect |
| 5. C8×C3⋊D9 | C2 | semidirect |
| 21. C9×Q16 | D3 | semidirect |
| 51. C3×Q16 | D9 | semidirect |
| 70. C3×C9 | #135 | semidirect |
| 92. Q16 | C3⋊D9 | semidirect |
| 107. C9 | #919 | semidirect |
| 126. C3 | #63481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #88746 | 2 |
| C3×C9×Q16 | 2 |
| #88548 | 2 |
| #88525 | 2 |
| C8×C3⋊D9 | 2 |
| #64128 | 3 |
| #63481 | 3 |