Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22581506 | C2 | semidirect |
| 3. #22581316 | C2 | semidirect |
| 4. #22581298 | C2 | semidirect |
| 5. #22580959 | C2 | semidirect |
| 6. #22580958 | C2 | semidirect |
| 7. #22580957 | C2 | semidirect |
| 8. M16×Dic139 | C2 | semidirect |
| 9. #418×C139 | C2 | semidirect |
| 13. #17984841 | C22 | semidirect |
| 17. #17984833 | C22 | semidirect |
| 22. #17984764 | C22 | semidirect |
| 23. #17984763 | C22 | semidirect |
| 24. #17984762 | C22 | semidirect |
| 25. #17984752 | C22 | semidirect |
| 26. C8×Dic139 | C22 | semidirect |
| 30. #102×C139 | C22 | semidirect |
| 111. C139 | #3138 | semidirect |
| 120. #418 | D139 | semidirect |
| 140. #102 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581506 | 2 |
| C2×#17984838 | 2 |
| #22581316 | 2 |
| #22581298 | 2 |
| #22580959 | 2 |
| #22580958 | 2 |
| #22580957 | 2 |
| M16×Dic139 | 2 |
| #418×C139 | 2 |
| #3138 | 139 |