Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
992 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 188 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 |
|---|---|---|
| 4. #11722055 | C2 | semidirect |
| 5. #11722040 | C2 | semidirect |
| 165. C33 | #484 | semidirect |
| 239. C32 | #4722 | semidirect |
| 240. C32 | #5044 | semidirect |
| 273. C3 | #10591103 | semidirect |
| 274. C3 | #10592421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| C3×#64133 | 2 |
| C32×#830 | 2 |
| #11722055 | 2 |
| #11722040 | 2 |
| #10592421 | 3 |
| #10591103 | 3 |