Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22562018 | C2 | semidirect |
| 3. #22560359 | C2 | semidirect |
| 5. #22558197 | C2 | semidirect |
| 7. C67×#1342 | C2 | semidirect |
| 9. #16863796 | C4 | semidirect |
| 10. #16863781 | C4 | semidirect |
| 14. #16863507 | C4 | semidirect |
| 15. #16863503 | C4 | semidirect |
| 143. #1342 | D67 | semidirect |
| 147. C67 | #11836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570939 | 2 |
| #22562018 | 2 |
| #22560359 | 2 |
| #22558199 | 2 |
| #22558197 | 2 |
| #22558195 | 2 |
| C67×#1342 | 2 |
| #11836 | 67 |