Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #22578031 | C2 | semidirect |
| 3. #22577768 | C2 | semidirect |
| 4. #22577763 | C2 | semidirect |
| 5. #22577758 | C2 | semidirect |
| 6. #22577750 | C2 | semidirect |
| 7. #22577409 | C2 | semidirect |
| 8. #22577405 | C2 | semidirect |
| 9. #22577400 | C2 | semidirect |
| 10. C2×#17984010 | C2 | semidirect |
| 11. #405×C137 | C2 | semidirect |
| 14. #17984088 | C22 | semidirect |
| 17. #17984080 | C22 | semidirect |
| 26. #17984013 | C22 | semidirect |
| 27. #17984013 | C22 | semidirect |
| 28. #17984013 | C22 | semidirect |
| 33. #17984010 | C22 | semidirect |
| 34. #17984010 | C22 | semidirect |
| 35. #17984010 | C22 | semidirect |
| 39. #97×C137 | C22 | semidirect |
| 40. C4×C8×C137 | C22 | semidirect |
| 135. C137 | #3136 | semidirect |
| 147. #405 | D137 | semidirect |
| 175. #97 | C2×D137 | semidirect |
| 176. C4×C8 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578031 | 2 |
| #22577972 | 2 |
| #22577768 | 2 |
| #22577763 | 2 |
| #22577758 | 2 |
| #22577750 | 2 |
| #22577409 | 2 |
| #22577405 | 2 |
| #22577400 | 2 |
| C2×#17984010 | 2 |
| #405×C137 | 2 |
| #3136 | 137 |