Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1078 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 191 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. #22568519 | C2 | semidirect |
| 3. #22561624 | C2 | semidirect |
| 4. #22561356 | C2 | semidirect |
| 5. #22560906 | C2 | semidirect |
| 6. #22560296 | C2 | semidirect |
| 8. C67×#1749 | C2 | semidirect |
| 10. C2×#14524035 | C22 | semidirect |
| 18. #16863294 | C22 | semidirect |
| 21. #16863262 | C22 | semidirect |
| 23. #16863159 | C22 | semidirect |
| 24. #16863159 | C22 | semidirect |
| 27. C2×#97×C67 | C22 | semidirect |
| 28. #336×C67 | C22 | semidirect |
| 188. #1749 | D67 | semidirect |
| 189. C67 | #29110 | semidirect |
| 198. C2×#97 | C2×D67 | semidirect |
| 209. #336 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568519 | 2 |
| C2×#16863298 | 2 |
| #22561624 | 2 |
| #22561356 | 2 |
| #22560906 | 2 |
| #22560296 | 2 |
| #22560141 | 2 |
| C67×#1749 | 2 |
| #29110 | 67 |