Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22581752 | C2 | semidirect |
| 2. C2×#17984865 | C2 | semidirect |
| 3. #131×D139 | C2 | semidirect |
| 4. #22581225 | C2 | semidirect |
| 5. #22581224 | C2 | semidirect |
| 6. #22581223 | C2 | semidirect |
| 7. #22581219 | C2 | semidirect |
| 8. #22581218 | C2 | semidirect |
| 9. #108×D139 | C2 | semidirect |
| 10. #22580936 | C2 | semidirect |
| 11. #473×C139 | C2 | semidirect |
| 25. C2×#14555772 | C22 | semidirect |
| 26. C2×D1112 | C22 | semidirect |
| 37. #17984778 | C22 | semidirect |
| 38. #17984777 | C22 | semidirect |
| 39. #17984761 | C22 | semidirect |
| 40. #17984758 | C22 | semidirect |
| 41. #17984758 | C22 | semidirect |
| 43. C2×Q16×C139 | C22 | semidirect |
| 45. #108×C139 | C22 | semidirect |
| 46. #101×C139 | C22 | semidirect |
| 166. C139 | #3067 | semidirect |
| 172. #473 | D139 | semidirect |
| 193. C2×Q16 | C2×D139 | semidirect |
| 209. #108 | C2×D139 | semidirect |
| 211. #101 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581752 | 2 |
| C2×#17984865 | 2 |
| #131×D139 | 2 |
| #22581225 | 2 |
| #22581224 | 2 |
| #22581223 | 2 |
| #22581219 | 2 |
| #22581218 | 2 |
| #108×D139 | 2 |
| #22580936 | 2 |
| #473×C139 | 2 |
| #3067 | 139 |