Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
414 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22558825 | C2 | semidirect |
| 4. #22558772 | C2 | semidirect |
| 5. #22558107 | C2 | semidirect |
| 6. #22558090 | C2 | semidirect |
| 9. #16863806 | C4 | semidirect |
| 10. #16863791 | C4 | semidirect |
| 11. #16863766 | C4 | semidirect |
| 12. #16863755 | C4 | semidirect |
| 206. C67 | #9431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570919 | 2 |
| #22569205 | 2 |
| #22558825 | 2 |
| #22558772 | 2 |
| #22558107 | 2 |
| #22558090 | 2 |
| C67×#1512 | 2 |
| #9431 | 67 |