Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22581508 | C2 | semidirect |
| 3. #22581315 | C2 | semidirect |
| 4. #22581313 | C2 | semidirect |
| 5. #22581312 | C2 | semidirect |
| 6. #22581309 | C2 | semidirect |
| 7. #22581306 | C2 | semidirect |
| 8. #22580960 | C2 | semidirect |
| 10. #22580905 | C2 | semidirect |
| 11. #489×C139 | C2 | semidirect |
| 15. #17984842 | C22 | semidirect |
| 16. #17984833 | C22 | semidirect |
| 30. #17984767 | C22 | semidirect |
| 31. #17984766 | C22 | semidirect |
| 32. #17984765 | C22 | semidirect |
| 36. #17984753 | C22 | semidirect |
| 37. C8×Dic139 | C22 | semidirect |
| 38. C4⋊Q8×C139 | C22 | semidirect |
| 40. #103×C139 | C22 | semidirect |
| 42. #97×C139 | C22 | semidirect |
| 138. C139 | #3140 | semidirect |
| 145. #489 | D139 | semidirect |
| 155. C4⋊Q8 | C2×D139 | semidirect |
| 174. #103 | C2×D139 | semidirect |
| 180. #97 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581508 | 2 |
| #124×D139 | 2 |
| #22581315 | 2 |
| #22581313 | 2 |
| #22581312 | 2 |
| #22581309 | 2 |
| #22581306 | 2 |
| #22580960 | 2 |
| #22580956 | 2 |
| #22580905 | 2 |
| #489×C139 | 2 |
| #3140 | 139 |