Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1132 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1132 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 |
|---|---|---|
| 1. #22574614 | C2 | semidirect |
| 2. #22571127 | C2 | semidirect |
| 3. #22559290 | C2 | semidirect |
| 4. #22559261 | C2 | semidirect |
| 5. #22558871 | C2 | semidirect |
| 6. #22558627 | C2 | semidirect |
| 7. C67×#3151 | C2 | semidirect |
| 9. #16864112 | C22 | semidirect |
| 12. #16864031 | C22 | semidirect |
| 18. #16863588 | C22 | semidirect |
| 20. #16863449 | C22 | semidirect |
| 21. #16863145 | C22 | semidirect |
| 22. #16863140 | C22 | semidirect |
| 23. #16863125 | C22 | semidirect |
| 26. C2×#127×C67 | C22 | semidirect |
| 29. #492×C67 | C22 | semidirect |
| 30. C4×M16×C67 | C22 | semidirect |
| 182. #3151 | D67 | semidirect |
| 187. C67 | #18714 | semidirect |
| 198. C2×#127 | C2×D67 | semidirect |
| 202. #492 | C2×D67 | semidirect |
| 207. C4×M16 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574614 | 2 |
| #22571127 | 2 |
| #22559290 | 2 |
| #22559261 | 2 |
| #22558871 | 2 |
| #22558627 | 2 |
| C67×#3151 | 2 |
| #18714 | 67 |