Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
516 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 516 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 |
|---|---|---|
| 2. #22561187 | C2 | semidirect |
| 4. C4×C8×Dic67 | C2 | semidirect |
| 5. #22558964 | C2 | semidirect |
| 7. C67×#1493 | C2 | semidirect |
| 9. #16863792 | C4 | semidirect |
| 10. #16863770 | C4 | semidirect |
| 11. #16863746 | C4 | semidirect |
| 12. #16863744 | C4 | semidirect |
| 88. C4×Dic67 | SD16 | semidirect |
| 141. C67⋊C8 | #104 | semidirect |
| 171. #1493 | D67 | semidirect |
| 173. C67 | #9843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570769 | 2 |
| #22561187 | 2 |
| #22561036 | 2 |
| C4×C8×Dic67 | 2 |
| #22558964 | 2 |
| #22558661 | 2 |
| C67×#1493 | 2 |
| #9843 | 67 |