Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
996 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22571592 | C2 | semidirect |
| 3. #22559434 | C2 | semidirect |
| 4. #22559385 | C2 | semidirect |
| 5. #22558944 | C2 | semidirect |
| 6. #22558661 | C2 | semidirect |
| 7. C67×#3131 | C2 | semidirect |
| 17. #16863673 | C22 | semidirect |
| 19. #16863598 | C22 | semidirect |
| 21. #16863420 | C22 | semidirect |
| 22. #16863145 | C22 | semidirect |
| 24. #16863125 | C22 | semidirect |
| 25. #533×C67 | C22 | semidirect |
| 28. #487×C67 | C22 | semidirect |
| 31. C2×C4×C8×C67 | C22 | semidirect |
| 182. #3131 | D67 | semidirect |
| 187. C67 | #18691 | semidirect |
| 195. #533 | C2×D67 | semidirect |
| 199. #487 | C2×D67 | semidirect |
| 208. C2×C4×C8 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574614 | 2 |
| #22571592 | 2 |
| #22559434 | 2 |
| #22559385 | 2 |
| #22558944 | 2 |
| #22558661 | 2 |
| C67×#3131 | 2 |
| #18691 | 67 |