Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
460 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #22559955 | C2 | semidirect |
| 4. #22558964 | C2 | semidirect |
| 5. #22558664 | C2 | semidirect |
| 7. C67×#1994 | C2 | semidirect |
| 9. #16863792 | C4 | semidirect |
| 10. #16863770 | C4 | semidirect |
| 11. #16863746 | C4 | semidirect |
| 12. #16863744 | C4 | semidirect |
| 104. C42×C67 | SD16 | semidirect |
| 166. #1994 | D67 | semidirect |
| 172. C67 | #9846 | semidirect |
| 269. C42 | #11761615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570769 | 2 |
| #22561037 | 2 |
| #22559955 | 2 |
| #22558964 | 2 |
| #22558664 | 2 |
| #22558659 | 2 |
| C67×#1994 | 2 |
| #9846 | 67 |