Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 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. #22581767 | C2 | semidirect |
| 2. #22581765 | C2 | semidirect |
| 3. #22581755 | C2 | semidirect |
| 4. #22581337 | C2 | semidirect |
| 5. #22581229 | C2 | semidirect |
| 6. #22581224 | C2 | semidirect |
| 7. #22581216 | C2 | semidirect |
| 8. #22581132 | C2 | semidirect |
| 9. #22581127 | C2 | semidirect |
| 10. #22581071 | C2 | semidirect |
| 11. #443×C139 | C2 | semidirect |
| 12. #17984889 | C22 | semidirect |
| 16. #17984872 | C22 | semidirect |
| 19. #17984870 | C22 | semidirect |
| 26. C2×Dic556 | C22 | semidirect |
| 29. C2×#14555774 | C22 | semidirect |
| 33. #17984848 | C22 | semidirect |
| 34. #17984830 | C22 | semidirect |
| 35. #17984778 | C22 | semidirect |
| 37. #17984770 | C22 | semidirect |
| 38. #17984760 | C22 | semidirect |
| 39. #17984758 | C22 | semidirect |
| 41. #131×C139 | C22 | semidirect |
| 42. #108×C139 | C22 | semidirect |
| 43. #104×C139 | C22 | semidirect |
| 44. C4×C8×C139 | C22 | semidirect |
| 149. C139 | #3290 | semidirect |
| 161. #443 | D139 | semidirect |
| 185. #131 | C2×D139 | semidirect |
| 188. #108 | C2×D139 | semidirect |
| 191. #104 | C2×D139 | semidirect |
| 194. C4×C8 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581767 | 2 |
| #22581765 | 2 |
| #22581755 | 2 |
| #22581337 | 2 |
| #22581229 | 2 |
| #22581224 | 2 |
| #22581216 | 2 |
| #22581132 | 2 |
| #22581127 | 2 |
| #22581071 | 2 |
| #443×C139 | 2 |
| #3290 | 139 |