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. #22581761 | C2 | semidirect |
| 2. #22581755 | C2 | semidirect |
| 3. #22581338 | C2 | semidirect |
| 4. #22581225 | C2 | semidirect |
| 5. #22581223 | C2 | semidirect |
| 6. #22581218 | C2 | semidirect |
| 7. #22581129 | C2 | semidirect |
| 8. #22581126 | C2 | semidirect |
| 9. #22581070 | C2 | semidirect |
| 10. #22581068 | C2 | semidirect |
| 11. #578×C139 | C2 | semidirect |
| 18. #17984867 | C22 | semidirect |
| 23. C2×#14555772 | C22 | semidirect |
| 26. #17984849 | C22 | semidirect |
| 28. #17984831 | C22 | semidirect |
| 29. #17984778 | C22 | semidirect |
| 30. #17984777 | C22 | semidirect |
| 31. #17984769 | C22 | semidirect |
| 32. #17984769 | C22 | semidirect |
| 34. #17984761 | C22 | semidirect |
| 35. #17984758 | C22 | semidirect |
| 36. C8×Dic139 | C22 | semidirect |
| 37. 2−1+4×C139 | C22 | semidirect |
| 39. #137×C139 | C22 | semidirect |
| 43. C2×Q16×C139 | C22 | semidirect |
| 44. #131×C139 | C22 | semidirect |
| 149. C139 | #3290 | semidirect |
| 151. #578 | D139 | semidirect |
| 162. 2−1+4 | C2×D139 | semidirect |
| 167. #137 | C2×D139 | semidirect |
| 178. C2×Q16 | C2×D139 | semidirect |
| 185. #131 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581761 | 2 |
| #22581755 | 2 |
| #22581338 | 2 |
| #22581225 | 2 |
| #22581223 | 2 |
| #22581218 | 2 |
| #22581129 | 2 |
| #22581126 | 2 |
| #22581070 | 2 |
| #22581068 | 2 |
| #578×C139 | 2 |
| #3290 | 139 |