Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22581581 | C2 | semidirect |
| 2. #22581317 | C2 | semidirect |
| 3. #22581312 | C2 | semidirect |
| 4. #22581307 | C2 | semidirect |
| 5. #22581299 | C2 | semidirect |
| 6. #22580958 | C2 | semidirect |
| 7. #22580954 | C2 | semidirect |
| 8. #22580949 | C2 | semidirect |
| 9. C2×#17984763 | C2 | semidirect |
| 10. #22580909 | C2 | semidirect |
| 14. #17984842 | C22 | semidirect |
| 16. #17984834 | C22 | semidirect |
| 21. #17984766 | C22 | semidirect |
| 22. #17984766 | C22 | semidirect |
| 23. #17984766 | C22 | semidirect |
| 28. #17984763 | C22 | semidirect |
| 29. #17984763 | C22 | semidirect |
| 30. #17984763 | C22 | semidirect |
| 31. #17984753 | C22 | semidirect |
| 32. C4×C139⋊C8 | C22 | semidirect |
| 135. C139 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581581 | 2 |
| #22581317 | 2 |
| #22581312 | 2 |
| #22581307 | 2 |
| #22581299 | 2 |
| #22580958 | 2 |
| #22580954 | 2 |
| #22580949 | 2 |
| C2×#17984763 | 2 |
| #22580909 | 2 |
| #535×C139 | 2 |
| #3136 | 139 |