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. #22586892 | C2 | semidirect |
| 5. #22586760 | C2 | semidirect |
| 6. #22586206 | C2 | semidirect |
| 7. C71×#1287 | C2 | semidirect |
| 10. #17986408 | C4 | semidirect |
| 11. #17986408 | C4 | semidirect |
| 12. #17986359 | C4 | semidirect |
| 13. #17986359 | C4 | semidirect |
| 196. #1287 | 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 |
|---|---|
| #22599582 | 2 |
| #22597320 | 2 |
| #22586918 | 2 |
| #22586892 | 2 |
| #22586760 | 2 |
| #22586206 | 2 |
| C71×#1287 | 2 |
| #9369 | 71 |