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. #22581581 | C2 | semidirect |
| 3. #22581316 | C2 | semidirect |
| 4. #22581314 | C2 | semidirect |
| 5. #22581309 | C2 | semidirect |
| 6. #22581298 | C2 | semidirect |
| 7. #22580957 | C2 | semidirect |
| 8. #22580954 | C2 | semidirect |
| 9. C2×#17984764 | C2 | semidirect |
| 10. #22580908 | C2 | semidirect |
| 11. #416×C139 | C2 | semidirect |
| 15. #17984841 | C22 | semidirect |
| 18. #17984833 | C22 | semidirect |
| 26. #17984766 | C22 | semidirect |
| 29. #17984763 | C22 | semidirect |
| 32. #17984752 | C22 | semidirect |
| 33. C8×Dic139 | C22 | semidirect |
| 37. #103×C139 | C22 | semidirect |
| 38. #103×C139 | C22 | semidirect |
| 39. #102×C139 | C22 | semidirect |
| 40. #102×C139 | C22 | semidirect |
| 135. C139 | #3136 | semidirect |
| 145. #416 | D139 | semidirect |
| 166. #103 | C2×D139 | semidirect |
| 167. #103 | C2×D139 | semidirect |
| 173. #102 | C2×D139 | semidirect |
| 174. #102 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581581 | 2 |
| #22581517 | 2 |
| #22581316 | 2 |
| #22581314 | 2 |
| #22581309 | 2 |
| #22581298 | 2 |
| #22580957 | 2 |
| #22580954 | 2 |
| C2×#17984764 | 2 |
| #22580908 | 2 |
| #416×C139 | 2 |
| #3136 | 139 |