Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22581584 | C2 | semidirect |
| 3. #22581316 | C2 | semidirect |
| 4. #22581311 | C2 | semidirect |
| 5. #22581306 | C2 | semidirect |
| 6. #22581298 | C2 | semidirect |
| 7. #22580958 | C2 | semidirect |
| 8. #22580952 | C2 | semidirect |
| 9. #22580950 | C2 | semidirect |
| 10. #22580908 | C2 | semidirect |
| 11. C2×#102×C139 | C2 | semidirect |
| 15. #17984841 | C22 | semidirect |
| 18. #17984833 | C22 | semidirect |
| 26. #17984767 | C22 | semidirect |
| 27. #17984767 | C22 | semidirect |
| 28. #17984765 | C22 | semidirect |
| 29. #17984764 | C22 | semidirect |
| 30. #17984764 | C22 | semidirect |
| 33. #17984762 | C22 | semidirect |
| 34. #17984752 | C22 | semidirect |
| 35. C8×Dic139 | C22 | semidirect |
| 135. C139 | #3136 | semidirect |
| 146. C2×#102 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581584 | 2 |
| #22581520 | 2 |
| #22581316 | 2 |
| #22581311 | 2 |
| #22581306 | 2 |
| #22581298 | 2 |
| #22580958 | 2 |
| #22580952 | 2 |
| #22580950 | 2 |
| #22580908 | 2 |
| C2×#102×C139 | 2 |
| #3136 | 139 |