Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
892 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 892 conjugacy classes of subgroups — too many to draw. Only its 208 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 |
|---|---|---|
| 32. #6308 | C8 | semidirect |
| 34. C3×C3⋊(C3⋊C8) | Q8 | semidirect |
| 97. C3⋊(C3⋊C8) | Dic6 | semidirect |
| 152. C33 | C8×Q8 | semidirect |
| 216. C32 | C8×Dic6 | semidirect |
| 217. C32 | #4830 | semidirect |
| 244. C3 | #10590254 | semidirect |
| 245. C3 | #10592529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6308 | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| C32×C4⋊(C3⋊C8) | 2 |
| #11722050 | 2 |
| #11722018 | 2 |
| #10592529 | 3 |
| #10590254 | 3 |