Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
478 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22561182 | C2 | semidirect |
| 4. #22558889 | C2 | semidirect |
| 6. #22558068 | C2 | semidirect |
| 7. C67×#1275 | C2 | semidirect |
| 11. #16863794 | C4 | semidirect |
| 12. #16863743 | C4 | semidirect |
| 180. #1275 | D67 | semidirect |
| 181. C67 | #9287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571339 | 2 |
| #22568928 | 2 |
| #22561182 | 2 |
| #22558889 | 2 |
| #22558770 | 2 |
| #22558068 | 2 |
| C67×#1275 | 2 |
| #9287 | 67 |