Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 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 |
|---|---|---|
| 3. #22586853 | C2 | semidirect |
| 5. #22586812 | C2 | semidirect |
| 6. #22586168 | C2 | semidirect |
| 7. C71×#1287 | C2 | semidirect |
| 10. #17986404 | C4 | semidirect |
| 11. #17986397 | C4 | semidirect |
| 12. #17986346 | C4 | semidirect |
| 13. #17986346 | C4 | semidirect |
| 174. #1287 | D71 | semidirect |
| 176. C71 | #9279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599478 | 2 |
| #22597418 | 2 |
| #22586853 | 2 |
| #22586849 | 2 |
| #22586812 | 2 |
| #22586168 | 2 |
| C71×#1287 | 2 |
| #9279 | 71 |