Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
647 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 647 conjugacy classes of subgroups — too many to draw. Only its 105 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. A4×Dic18 | 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 | direct (N × H) |
| 54. C9×A4 | C2×Q8 | semidirect |
| 76. C23×C9 | C3×Q8 | semidirect |
| 96. Dic18 | C2×A4 | direct (N × H) |
| 137. C22×C9 | C2×C3×Q8 | semidirect |
| 160. C2×A4 | Dic18 | direct (N × H) |
| 189. C2×C9 | Q8×A4 | semidirect |
| 222. A4 | C2×Dic18 | direct (N × H) |
| 232. C9 | C2×Q8×A4 | semidirect |
| 236. C23 | C3×Dic18 | semidirect |
| 270. C22 | C2×C3×Dic18 | semidirect |
| 282. C2 | A4×Dic18 | 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×A4×Dic9 | 2 |
| A4×Dic18 | 2 |
| C2×A4×Dic6 | 3 |
| C23×Dic18 | 3 |
| C2×C3×Dic18 | 4 |