Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#17984866 | C2 | semidirect |
| 2. #22581501 | C2 | semidirect |
| 3. C4×D4×D139 | C2 | semidirect |
| 4. #22581167 | C2 | semidirect |
| 5. #22581166 | C2 | semidirect |
| 6. #22581159 | C2 | semidirect |
| 7. #22581158 | C2 | semidirect |
| 8. #22581145 | C2 | semidirect |
| 9. #22580975 | C2 | semidirect |
| 10. #22580951 | C2 | semidirect |
| 11. #459×C139 | C2 | semidirect |
| 20. #17984842 | C22 | semidirect |
| 21. #17984829 | C22 | semidirect |
| 34. C4⋊(C139⋊C8) | C22 | semidirect |
| 35. Dic139⋊C8 | C22 | semidirect |
| 36. #17984767 | C22 | semidirect |
| 37. #17984765 | C22 | semidirect |
| 38. #17984763 | C22 | semidirect |
| 40. #127×C139 | C22 | semidirect |
| 42. C4⋊C8×C139 | C22 | semidirect |
| 43. #102×C139 | C22 | semidirect |
| 52. D4×D139 | D4 | semidirect |
| 145. C4×C139 | AGL(1,ℤ/8) | semidirect |
| 160. C139 | #3036 | semidirect |
| 170. #459 | D139 | semidirect |
| 183. #127 | C2×D139 | semidirect |
| 200. C4⋊C8 | C2×D139 | semidirect |
| 204. #102 | C2×D139 | semidirect |
| 311. C4 | #17984866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984866 | 2 |
| #22581501 | 2 |
| C4×D4×D139 | 2 |
| #22581167 | 2 |
| #22581166 | 2 |
| #22581159 | 2 |
| #22581158 | 2 |
| #22581145 | 2 |
| #22580975 | 2 |
| #22580951 | 2 |
| #459×C139 | 2 |
| #3036 | 139 |