Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
627 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 627 conjugacy classes of subgroups — too many to draw. Only its 87 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. Q8×C9⋊A4 | C2 | semidirect |
| 3. Dic18⋊A4 | C2 | semidirect |
| 5. C22×Q8×D9 | C3 | semidirect |
| 13. C22×Q8×C9 | C2×C3 | semidirect |
| 19. C22×Dic18 | C2×C3 | semidirect |
| 22. D9⋊A4 | Q8 | direct (N × H) |
| 43. Q8×D9 | A4 | semidirect |
| 53. C9⋊A4 | C2×Q8 | semidirect |
| 75. C22×D9 | C3×Q8 | semidirect |
| 80. Q8×C9 | C2×A4 | semidirect |
| 93. Dic18 | C2×A4 | semidirect |
| 126. C22×C9 | C2×C3×Q8 | semidirect |
| 144. C22×Q8 | AGL(1,ℤ/9) | semidirect |
| 180. D9 | Q8×A4 | semidirect |
| 219. C9 | C2×Q8×A4 | semidirect |
| 231. Q8 | D9⋊A4 | direct (N × H) |
| 256. C22 | Q8×AGL(1,ℤ/9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C9⋊A4 | 2 |
| C4×D9⋊A4 | 2 |
| Dic18⋊A4 | 2 |
| D3×Q8×A4 | 3 |
| C22×Q8×D9 | 3 |
| Q8×AGL(1,ℤ/9) | 4 |