Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 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×#17984889 | C2 | semidirect |
| 2. #22581768 | C2 | semidirect |
| 3. #22581764 | C2 | semidirect |
| 4. #22581751 | C2 | semidirect |
| 5. C2×#17984872 | C2 | semidirect |
| 6. #22581720 | C2 | semidirect |
| 7. #585×C139 | C2 | semidirect |
| 9. #17984889 | C22 | semidirect |
| 10. C2×#14555785 | C22 | semidirect |
| 12. C22×Dic278 | C22 | semidirect |
| 14. #17984873 | C22 | semidirect |
| 15. #17984872 | C22 | semidirect |
| 16. #17984872 | C22 | semidirect |
| 17. #17984868 | C22 | semidirect |
| 18. #17984867 | C22 | semidirect |
| 19. #17984862 | C22 | semidirect |
| 20. C2×#14555775 | C22 | semidirect |
| 21. C2×#14555773 | C22 | semidirect |
| 22. #17984849 | C22 | semidirect |
| 23. C2×#14555769 | C22 | semidirect |
| 25. 2−1+4×C139 | C22 | semidirect |
| 27. H(5,𝔽2)×C139 | C22 | semidirect |
| 112. C139 | #3586 | semidirect |
| 114. #585 | D139 | semidirect |
| 124. 2−1+4 | C2×D139 | semidirect |
| 126. H(5,𝔽2) | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984889 | 2 |
| #22581768 | 2 |
| #22581764 | 2 |
| #22581751 | 2 |
| C2×#17984872 | 2 |
| #22581720 | 2 |
| #585×C139 | 2 |
| #3586 | 139 |