Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
384 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 10. #88521 | C4 | semidirect |
| 137. C3×C9 | #441 | semidirect |
| 191. C9 | #4853 | semidirect |
| 213. C3 | #10588384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88521 | 2 |
| #11720912 | 2 |
| C9×#815 | 2 |
| C3×#63377 | 2 |
| #11720277 | 2 |
| #10590810 | 3 |
| #10588384 | 3 |