Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
310 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 109 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. C3×C9×M16 | C2 | semidirect |
| 3. C2×C3⋊(C9⋊C8) | C2 | semidirect |
| 4. #88523 | C2 | semidirect |
| 5. C8×C3⋊D9 | C2 | semidirect |
| 22. C9×M16 | D3 | semidirect |
| 54. C3×M16 | D9 | semidirect |
| 73. C3×C9 | #131 | semidirect |
| 98. M16 | C3⋊D9 | semidirect |
| 112. C9 | #907 | semidirect |
| 132. C3 | #63469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #88736 | 2 |
| C3×C9×M16 | 2 |
| C2×C3⋊(C9⋊C8) | 2 |
| #88523 | 2 |
| C8×C3⋊D9 | 2 |
| #64116 | 3 |
| #63469 | 3 |