Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 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. #22577886 | C2 | semidirect |
| 2. #22577724 | C2 | semidirect |
| 3. #22577724 | C2 | semidirect |
| 4. #22577719 | C2 | semidirect |
| 5. #22577714 | C2 | semidirect |
| 6. #22577446 | C2 | semidirect |
| 7. #22577439 | C2 | semidirect |
| 8. #22577408 | C2 | semidirect |
| 9. C2×#17984009 | C2 | semidirect |
| 10. #22577370 | C2 | semidirect |
| 18. #17984047 | C22 | semidirect |
| 20. C2×C4⋊Dic137 | C22 | semidirect |
| 21. #17984021 | C22 | semidirect |
| 22. #17984021 | C22 | semidirect |
| 23. #17984021 | C22 | semidirect |
| 24. #17984019 | C22 | semidirect |
| 25. #17984019 | C22 | semidirect |
| 26. #17984019 | C22 | semidirect |
| 31. C22⋊#11764040 | C22 | semidirect |
| 32. C22⋊#11764040 | C22 | semidirect |
| 134. C137 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577886 | 2 |
| #22577724 | 2 |
| #22577719 | 2 |
| #22577714 | 2 |
| #22577446 | 2 |
| #22577439 | 2 |
| #22577408 | 2 |
| C2×#17984009 | 2 |
| #22577370 | 2 |
| #535×C137 | 2 |
| #3096 | 137 |