Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
424 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 9. #17986405 | C4 | semidirect |
| 10. #17986367 | C4 | semidirect |
| 188. C71 | #9380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599542 | 2 |
| #22591141 | 2 |
| #22589285 | 2 |
| #22586943 | 2 |
| #22586204 | 2 |
| #22586197 | 2 |
| C71×#1515 | 2 |
| #9380 | 71 |