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. #22581749 | C2 | semidirect |
| 2. C2×#17984861 | C2 | semidirect |
| 3. #131×D139 | C2 | semidirect |
| 4. #22581229 | C2 | semidirect |
| 5. #22581228 | C2 | semidirect |
| 6. #22581220 | C2 | semidirect |
| 7. #22581215 | C2 | semidirect |
| 8. #22581214 | C2 | semidirect |
| 9. #108×D139 | C2 | semidirect |
| 10. #22580934 | C2 | semidirect |
| 11. #472×C139 | C2 | semidirect |
| 25. C2×Dic556 | C22 | semidirect |
| 26. C2×#14555773 | C22 | semidirect |
| 37. #17984778 | C22 | semidirect |
| 38. #17984777 | C22 | semidirect |
| 39. #17984760 | C22 | semidirect |
| 40. #17984760 | C22 | semidirect |
| 41. #17984759 | C22 | semidirect |
| 43. C2×D8×C139 | C22 | semidirect |
| 45. #108×C139 | C22 | semidirect |
| 46. #100×C139 | C22 | semidirect |
| 166. C139 | #3067 | semidirect |
| 174. #472 | D139 | semidirect |
| 195. C2×D8 | C2×D139 | semidirect |
| 209. #108 | C2×D139 | semidirect |
| 213. #100 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581749 | 2 |
| C2×#17984861 | 2 |
| #131×D139 | 2 |
| #22581229 | 2 |
| #22581228 | 2 |
| #22581220 | 2 |
| #22581215 | 2 |
| #22581214 | 2 |
| #108×D139 | 2 |
| #22580934 | 2 |
| #472×C139 | 2 |
| #3067 | 139 |