Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1372 conjugacy classes of subgroups; only the 411 normal subgroups are shown.
This group has 1372 conjugacy classes of subgroups — too many to draw. Only its 411 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 |
|---|---|---|
| 25. C33×C8 | Q8 | semidirect |
| 26. C3⋊(C3⋊(C3⋊C8)) | Q8 | semidirect |
| 53. C32×C8 | Dic6 | semidirect |
| 78. C33 | #500 | semidirect |
| 85. C3×C8 | #634 | semidirect |
| 104. C32 | #4874 | semidirect |
| 112. C8 | #6308 | semidirect |
| 123. C3 | #10592573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723929 | 2 |
| C33×#107 | 2 |
| #11722188 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| #11722177 | 2 |
| #10592573 | 3 |