Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22561185 | C2 | semidirect |
| 4. #22559954 | C2 | semidirect |
| 5. #22558964 | C2 | semidirect |
| 6. #22558665 | C2 | semidirect |
| 9. #16863792 | C4 | semidirect |
| 10. #16863768 | C4 | semidirect |
| 11. #16863748 | C4 | semidirect |
| 12. #16863742 | C4 | semidirect |
| 85. C4×Dic67 | SD16 | semidirect |
| 172. C67 | #9846 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570764 | 2 |
| #22561185 | 2 |
| #22561038 | 2 |
| #22559954 | 2 |
| #22558964 | 2 |
| #22558665 | 2 |
| C67×#1492 | 2 |
| #9846 | 67 |