Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
494 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. C2×#88427 | C2 | semidirect |
| 5. #11720268 | C2 | semidirect |
| 71. C22×C3×C9 | Q16 | semidirect |
| 164. C22×C9 | #216 | semidirect |
| 178. C3×C9 | #451 | semidirect |
| 241. C22×C3 | #3674 | semidirect |
| 259. C9 | #5228 | semidirect |
| 287. C22 | #88427 | semidirect |
| 295. C3 | #10588726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic18 | 2 |
| C9×#924 | 2 |
| C2×#88427 | 2 |
| #11720571 | 2 |
| #11720268 | 2 |
| #10591185 | 3 |
| #10588726 | 3 |