Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
631 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 631 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. Dic18⋊A4 | C2 | direct (N × H) |
| 5. C23×Dic18 | C3 | semidirect |
| 19. C22×Dic18 | C2×C3 | semidirect |
| 21. C2×C9⋊A4 | Q8 | semidirect |
| 51. C2×Dic18 | A4 | semidirect |
| 54. C9⋊A4 | C2×Q8 | semidirect |
| 75. C23×C9 | C3×Q8 | semidirect |
| 95. Dic18 | C2×A4 | semidirect |
| 134. C22×C9 | C2×C3×Q8 | semidirect |
| 183. C2×C9 | Q8×A4 | semidirect |
| 223. C9 | C2×Q8×A4 | semidirect |
| 227. C23 | 3−1+2⋊Q8 | semidirect |
| 259. C22 | C2×3−1+2⋊Q8 | semidirect |
| 270. C2 | Dic18⋊A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C9⋊A4 | 2 |
| C2×Dic9⋊A4 | 2 |
| Dic18⋊A4 | 2 |
| C2×A4×Dic6 | 3 |
| C23×Dic18 | 3 |
| C2×3−1+2⋊Q8 | 4 |