Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
992 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 1. #22599351 | C2 | semidirect |
| 2. #22598685 | C2 | semidirect |
| 3. #22587646 | C2 | semidirect |
| 4. #22586975 | C2 | semidirect |
| 5. #22586951 | C2 | semidirect |
| 7. #17986556 | C22 | semidirect |
| 8. #17986394 | C22 | semidirect |
| 11. #17986358 | C22 | semidirect |
| 12. #17986358 | C22 | semidirect |
| 16. #17986056 | C22 | semidirect |
| 18. C2×#14556039 | C22 | semidirect |
| 19. #17985739 | C22 | semidirect |
| 20. #17985739 | C22 | semidirect |
| 177. C71 | #19056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599351 | 2 |
| #22598685 | 2 |
| #22587646 | 2 |
| #22586975 | 2 |
| #22586951 | 2 |
| C71×#3549 | 2 |
| #19056 | 71 |