Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
530 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 6. #10590902 | C3 | direct (N × H) |
| 29. C33×C8 | Q8 | semidirect |
| 30. C3×C3⋊(C3⋊C8) | Q8 | semidirect |
| 89. C32×C8 | Dic6 | semidirect |
| 90. C32×C8 | C3×Q8 | semidirect |
| 91. C3⋊(C3⋊C8) | C3×Q8 | semidirect |
| 146. C33 | #500 | semidirect |
| 168. C3×C8 | #627 | semidirect |
| 169. C3×C8 | C3×Dic6 | semidirect |
| 221. C32 | #4874 | semidirect |
| 222. C32 | C3×#500 | semidirect |
| 229. C8 | C3×#627 | semidirect |
| 254. C3 | #10590902 | direct (N × H) |
| 255. C3 | C3×#4874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63919 | 2 |
| C3×C8×C3⋊Dic3 | 2 |
| C32×#818 | 2 |
| C3×#63576 | 2 |
| C3×#4874 | 3 |
| #10590902 | 3 |