Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22558663 | C2 | semidirect |
| 7. C67×#1566 | C2 | semidirect |
| 10. #16863794 | C4 | semidirect |
| 11. #16863769 | C4 | semidirect |
| 12. #16863747 | C4 | semidirect |
| 13. #16863743 | C4 | semidirect |
| 94. C4×Dic67 | SD16 | semidirect |
| 169. #1566 | D67 | semidirect |
| 172. C67 | #9846 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570768 | 2 |
| #22561185 | 2 |
| #22561036 | 2 |
| #22559954 | 2 |
| #22558663 | 2 |
| #22558659 | 2 |
| C67×#1566 | 2 |
| #9846 | 67 |