Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1056 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1056 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. #22571334 | C2 | semidirect |
| 2. #22570669 | C2 | semidirect |
| 3. #22559354 | C2 | semidirect |
| 4. #22559325 | C2 | semidirect |
| 5. #22558871 | C2 | semidirect |
| 6. #22558626 | C2 | semidirect |
| 9. C2×#14524043 | C22 | semidirect |
| 12. #16863775 | C22 | semidirect |
| 16. #16863686 | C22 | semidirect |
| 17. #16863449 | C22 | semidirect |
| 18. C4×#11761612 | C22 | semidirect |
| 19. #16863145 | C22 | semidirect |
| 21. D4⋊(C67⋊C8) | C22 | semidirect |
| 179. C67 | #18715 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571334 | 2 |
| #22570669 | 2 |
| #22559354 | 2 |
| #22559325 | 2 |
| #22558871 | 2 |
| #22558626 | 2 |
| C67×#3549 | 2 |
| #18715 | 67 |