Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
390 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22586891 | C2 | semidirect |
| 5. #22586205 | C2 | semidirect |
| 6. #22586202 | C2 | semidirect |
| 7. C71×#1485 | C2 | semidirect |
| 9. #17986405 | C4 | semidirect |
| 10. #17986405 | C4 | semidirect |
| 11. #17986361 | C4 | semidirect |
| 12. #17986361 | C4 | semidirect |
| 194. #1485 | D71 | semidirect |
| 197. C71 | #9369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599580 | 2 |
| #22597325 | 2 |
| #22586918 | 2 |
| #22586891 | 2 |
| #22586205 | 2 |
| #22586202 | 2 |
| C71×#1485 | 2 |
| #9369 | 71 |