Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22586852 | C2 | semidirect |
| 5. #22586201 | C2 | semidirect |
| 6. #22586168 | C2 | semidirect |
| 7. C71×#1497 | C2 | semidirect |
| 9. #17986402 | C4 | semidirect |
| 10. #17986395 | C4 | semidirect |
| 11. #17986347 | C4 | semidirect |
| 12. #17986347 | C4 | semidirect |
| 173. #1497 | D71 | semidirect |
| 176. C71 | #9279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599476 | 2 |
| #22597415 | 2 |
| #22586852 | 2 |
| #22586849 | 2 |
| #22586201 | 2 |
| #22586168 | 2 |
| C71×#1497 | 2 |
| #9279 | 71 |