Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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×#17984871 | C2 | semidirect |
| 2. C2×#17984866 | C2 | semidirect |
| 3. #22581501 | C2 | semidirect |
| 4. #124×D139 | C2 | semidirect |
| 5. #22581348 | C2 | semidirect |
| 6. #22581347 | C2 | semidirect |
| 7. #22581340 | C2 | semidirect |
| 8. #22581336 | C2 | semidirect |
| 9. #22581334 | C2 | semidirect |
| 10. #22580905 | C2 | semidirect |
| 11. #496×C139 | C2 | semidirect |
| 17. C2×Dic556 | C22 | semidirect |
| 18. C2×#14555775 | C22 | semidirect |
| 21. C2×#14555773 | C22 | semidirect |
| 24. #17984842 | C22 | semidirect |
| 28. #17984829 | C22 | semidirect |
| 34. #17984753 | C22 | semidirect |
| 35. C8×Dic139 | C22 | semidirect |
| 36. C2×SD16×C139 | C22 | semidirect |
| 38. #127×C139 | C22 | semidirect |
| 40. #97×C139 | C22 | semidirect |
| 62. #14555768 | D4 | semidirect |
| 134. C139 | #3153 | semidirect |
| 143. #496 | D139 | semidirect |
| 157. C2×SD16 | C2×D139 | semidirect |
| 162. #127 | C2×D139 | semidirect |
| 174. #97 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984871 | 2 |
| C2×#17984866 | 2 |
| #22581501 | 2 |
| #124×D139 | 2 |
| #22581348 | 2 |
| #22581347 | 2 |
| #22581340 | 2 |
| #22581336 | 2 |
| #22581334 | 2 |
| #22580905 | 2 |
| #496×C139 | 2 |
| #3153 | 139 |