Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1082 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22571587 | C2 | semidirect |
| 2. #22570635 | C2 | semidirect |
| 3. #22559354 | C2 | semidirect |
| 4. #22559325 | C2 | semidirect |
| 5. #22559292 | C2 | semidirect |
| 6. #22559263 | C2 | semidirect |
| 7. #22558944 | C2 | semidirect |
| 8. #22558660 | C2 | semidirect |
| 9. C67×#3549 | C2 | semidirect |
| 11. #16863946 | C22 | semidirect |
| 13. #16863775 | C22 | semidirect |
| 15. #16863770 | C22 | semidirect |
| 17. #16863686 | C22 | semidirect |
| 20. #16863591 | C22 | semidirect |
| 22. #16863420 | C22 | semidirect |
| 23. C2×C4×C67⋊C8 | C22 | semidirect |
| 24. #16863145 | C22 | semidirect |
| 26. D4⋊(C67⋊C8) | C22 | semidirect |
| 27. D4⋊(C67⋊C8) | C22 | semidirect |
| 206. #3549 | D67 | semidirect |
| 215. C67 | #18686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571587 | 2 |
| #22570635 | 2 |
| #22559354 | 2 |
| #22559325 | 2 |
| #22559292 | 2 |
| #22559263 | 2 |
| #22558944 | 2 |
| #22558660 | 2 |
| C67×#3549 | 2 |
| #18686 | 67 |