Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #22577883 | C2 | semidirect |
| 3. #22577726 | C2 | semidirect |
| 4. #22577725 | C2 | semidirect |
| 5. #22577720 | C2 | semidirect |
| 6. #22577715 | C2 | semidirect |
| 7. #22577445 | C2 | semidirect |
| 8. #22577439 | C2 | semidirect |
| 9. C2×#17984009 | C2 | semidirect |
| 10. #22577371 | C2 | semidirect |
| 11. #418×C137 | C2 | semidirect |
| 23. #17984046 | C22 | semidirect |
| 25. C4⋊C4×D137 | C22 | semidirect |
| 26. #17984022 | C22 | semidirect |
| 27. #17984021 | C22 | semidirect |
| 28. #17984021 | C22 | semidirect |
| 29. #17984020 | C22 | semidirect |
| 30. #17984019 | C22 | semidirect |
| 31. #17984019 | C22 | semidirect |
| 34. #17984000 | C22 | semidirect |
| 35. #17984000 | C22 | semidirect |
| 134. C137 | #3096 | semidirect |
| 144. #418 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577970 | 2 |
| #22577883 | 2 |
| #22577726 | 2 |
| #22577725 | 2 |
| #22577720 | 2 |
| #22577715 | 2 |
| #22577445 | 2 |
| #22577439 | 2 |
| C2×#17984009 | 2 |
| #22577371 | 2 |
| #418×C137 | 2 |
| #3096 | 137 |