Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
320 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 102. C3×C9 | #332 | semidirect |
| 146. C9 | #4547 | semidirect |
| 168. C3 | #10588224 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×C4⋊Q8 | 2 |
| C4⋊(C3⋊(C9⋊C8)) | 2 |
| #10589413 | 3 |
| #10588224 | 3 |