Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2786 conjugacy classes of subgroups; only the 1629 normal subgroups are shown.
This group has 2786 conjugacy classes of subgroups — too many to draw. Only its 1629 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. C22×C9×Dic6 | C2 | direct (N × H) |
| 9. C2×C9×Dic6 | C22 | direct (N × H) |
| 17. C23×C3×C9 | Q8 | semidirect |
| 21. C9×Dic6 | C23 | direct (N × H) |
| 23. C23×Dic6 | C9 | direct (N × H) |
| 34. C22×C3×C9 | C2×Q8 | semidirect |
| 44. C22×Dic6 | C2×C9 | direct (N × H) |
| 52. C23×C9 | Dic6 | direct (N × H) |
| 59. C2×C3×C9 | C22×Q8 | semidirect |
| 70. C2×Dic6 | C22×C9 | direct (N × H) |
| 77. C22×C9 | C2×Dic6 | direct (N × H) |
| 85. C3×C9 | C23×Q8 | semidirect |
| 88. C23×C3 | Q8×C9 | semidirect |
| 98. Dic6 | C23×C9 | direct (N × H) |
| 103. C2×C9 | C22×Dic6 | direct (N × H) |
| 111. C22×C3 | C2×Q8×C9 | semidirect |
| 122. C9 | C23×Dic6 | direct (N × H) |
| 123. C23 | C9×Dic6 | direct (N × H) |
| 130. C2×C3 | C22×Q8×C9 | semidirect |
| 134. C22 | C2×C9×Dic6 | direct (N × H) |
| 139. C3 | C23×Q8×C9 | semidirect |
| 141. C2 | C22×C9×Dic6 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C4×C9 | 2 |
| C23×C9×Dic3 | 2 |
| C22×C9×Dic6 | 2 |
| C23×C3×Dic6 | 3 |
| C23×Q8×C9 | 3 |