Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
434 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22561131 | C2 | semidirect |
| 4. #22558925 | C2 | semidirect |
| 6. #22558064 | C2 | semidirect |
| 7. C67×#1290 | C2 | semidirect |
| 10. #16863805 | C4 | semidirect |
| 11. #16863756 | C4 | semidirect |
| 200. #1290 | D67 | semidirect |
| 202. C67 | #9377 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571441 | 2 |
| #22569345 | 2 |
| #22561131 | 2 |
| #22558925 | 2 |
| #22558735 | 2 |
| #22558064 | 2 |
| C67×#1290 | 2 |
| #9377 | 67 |