Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
1424 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1424 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. #22581789 | C2 | semidirect |
| 2. #22581770 | C2 | semidirect |
| 3. #22581765 | C2 | semidirect |
| 4. #22581758 | C2 | semidirect |
| 5. #22581753 | C2 | semidirect |
| 6. C2×#17984864 | C2 | semidirect |
| 7. C2×#131×C139 | C2 | semidirect |
| 9. #17984889 | C22 | semidirect |
| 10. #17984888 | C22 | semidirect |
| 12. C2×#14555785 | C22 | semidirect |
| 14. #17984875 | C22 | semidirect |
| 15. #17984870 | C22 | semidirect |
| 16. #17984864 | C22 | semidirect |
| 17. #17984864 | C22 | semidirect |
| 18. #17984864 | C22 | semidirect |
| 19. #17984864 | C22 | semidirect |
| 20. C2×Dic556 | C22 | semidirect |
| 21. C2×#14555774 | C22 | semidirect |
| 22. C2×D1112 | C22 | semidirect |
| 24. #131×C139 | C22 | semidirect |
| 25. #131×C139 | C22 | semidirect |
| 26. C2×M16×C139 | C22 | semidirect |
| 27. C22×C8×C139 | C22 | semidirect |
| 89. C139 | #3584 | semidirect |
| 97. C2×#131 | D139 | semidirect |
| 114. #131 | C2×D139 | semidirect |
| 115. #131 | C2×D139 | semidirect |
| 116. C2×M16 | C2×D139 | semidirect |
| 117. C22×C8 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581789 | 2 |
| #22581770 | 2 |
| #22581765 | 2 |
| #22581758 | 2 |
| #22581753 | 2 |
| C2×#17984864 | 2 |
| C2×#131×C139 | 2 |
| #3584 | 139 |