Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
656 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 198 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. #10589413 | C3 | direct (N × H) |
| 125. C33 | #332 | semidirect |
| 185. C32 | #4547 | semidirect |
| 186. C32 | C3×#332 | semidirect |
| 212. C3 | C3×#4547 | semidirect |
| 213. C3 | #10589413 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4⋊Q8 | 2 |
| C3×C4⋊(C3⋊(C3⋊C8)) | 2 |
| #10589413 | 3 |
| C3×#4547 | 3 |