Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 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. #22581766 | C2 | semidirect |
| 2. #22581759 | C2 | semidirect |
| 3. #22581754 | C2 | semidirect |
| 4. #22581225 | C2 | semidirect |
| 5. #22581220 | C2 | semidirect |
| 6. #22581213 | C2 | semidirect |
| 7. #22581130 | C2 | semidirect |
| 8. #22581125 | C2 | semidirect |
| 9. #22581071 | C2 | semidirect |
| 10. #22581071 | C2 | semidirect |
| 11. #495×C139 | C2 | semidirect |
| 12. #17984890 | C22 | semidirect |
| 16. #17984873 | C22 | semidirect |
| 20. #17984868 | C22 | semidirect |
| 31. #17984848 | C22 | semidirect |
| 32. #17984848 | C22 | semidirect |
| 33. #17984778 | C22 | semidirect |
| 34. #17984778 | C22 | semidirect |
| 36. #17984770 | C22 | semidirect |
| 37. #17984770 | C22 | semidirect |
| 38. #17984761 | C22 | semidirect |
| 39. #17984759 | C22 | semidirect |
| 40. C2×Q16×C139 | C22 | semidirect |
| 41. C2×SD16×C139 | C22 | semidirect |
| 43. #124×C139 | C22 | semidirect |
| 44. C4×C8×C139 | C22 | semidirect |
| 149. C139 | #3290 | semidirect |
| 154. #495 | D139 | semidirect |
| 178. C2×Q16 | C2×D139 | semidirect |
| 180. C2×SD16 | C2×D139 | semidirect |
| 186. #124 | 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 |
|---|---|
| #22581766 | 2 |
| #22581759 | 2 |
| #22581754 | 2 |
| #22581225 | 2 |
| #22581220 | 2 |
| #22581213 | 2 |
| #22581130 | 2 |
| #22581125 | 2 |
| #22581071 | 2 |
| #495×C139 | 2 |
| #3290 | 139 |