Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
418 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22589293 | C2 | semidirect |
| 5. #22586209 | C2 | semidirect |
| 6. #22586197 | C2 | semidirect |
| 7. C71×#1558 | C2 | semidirect |
| 9. #17986405 | C4 | semidirect |
| 10. #17986361 | C4 | semidirect |
| 192. #1558 | D71 | semidirect |
| 196. C71 | #9375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599561 | 2 |
| #22597481 | 2 |
| #22589293 | 2 |
| #22586866 | 2 |
| #22586209 | 2 |
| #22586197 | 2 |
| C71×#1558 | 2 |
| #9375 | 71 |