Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
766 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22581788 | C2 | semidirect |
| 2. #22581459 | C2 | semidirect |
| 3. #22581144 | C2 | semidirect |
| 4. #22581143 | C2 | semidirect |
| 5. #22581139 | C2 | semidirect |
| 6. #22580925 | C2 | semidirect |
| 7. B(4,𝔽2)×C139 | C2 | semidirect |
| 14. C23×Dic139 | C22 | semidirect |
| 15. #17984826 | C22 | semidirect |
| 16. #17984823 | C22 | semidirect |
| 19. #17984811 | C22 | semidirect |
| 22. #17984798 | C22 | semidirect |
| 23. #17984757 | C22 | semidirect |
| 24. #17984756 | C22 | semidirect |
| 26. #120×C139 | C22 | semidirect |
| 27. #99×C139 | C22 | semidirect |
| 37. C2×Dic278 | D4 | semidirect |
| 42. C2×C22⋊D139 | D4 | semidirect |
| 49. C22×Dic139 | D4 | semidirect |
| 53. C2×C4×D139 | D4 | semidirect |
| 126. C139 | #3025 | semidirect |
| 133. B(4,𝔽2) | D139 | semidirect |
| 148. #120 | C2×D139 | semidirect |
| 154. #99 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581788 | 2 |
| #22581459 | 2 |
| #22581144 | 2 |
| #22581143 | 2 |
| #22581139 | 2 |
| #22580925 | 2 |
| B(4,𝔽2)×C139 | 2 |
| #3025 | 139 |