Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
450 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. #22586934 | C2 | semidirect |
| 5. #22586851 | C2 | semidirect |
| 6. #22586211 | C2 | semidirect |
| 7. C71×#1300 | C2 | semidirect |
| 11. #17986295 | C4 | semidirect |
| 12. #17986290 | C4 | semidirect |
| 13. #17986210 | C4 | semidirect |
| 14. #17986205 | C4 | semidirect |
| 200. #1300 | D71 | semidirect |
| 202. C71 | #9160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598503 | 2 |
| #22597358 | 2 |
| #22588151 | 2 |
| #22586934 | 2 |
| #22586851 | 2 |
| #22586211 | 2 |
| C71×#1300 | 2 |
| #9160 | 71 |