Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22586220 | C2 | semidirect |
| 5. #22586218 | C2 | semidirect |
| 6. #22586207 | C2 | semidirect |
| 7. C71×#1289 | C2 | semidirect |
| 14. #17985866 | C4 | semidirect |
| 15. #17985861 | C4 | semidirect |
| 18. #17985846 | C4 | semidirect |
| 19. #17985844 | C4 | semidirect |
| 234. #1289 | D71 | semidirect |
| 235. C71 | #8763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22591282 | 2 |
| #22588325 | 2 |
| #22586656 | 2 |
| #22586220 | 2 |
| #22586218 | 2 |
| #22586207 | 2 |
| C71×#1289 | 2 |
| #8763 | 71 |