Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
430 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 430 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. #22561158 | C2 | semidirect |
| 5. #22558078 | C2 | semidirect |
| 6. #22558066 | C2 | semidirect |
| 7. C67×#1556 | C2 | semidirect |
| 9. #16863788 | C4 | semidirect |
| 10. #16863764 | C4 | semidirect |
| 193. #1556 | D67 | semidirect |
| 197. C67 | #9376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571236 | 2 |
| #22569350 | 2 |
| #22561158 | 2 |
| #22558735 | 2 |
| #22558078 | 2 |
| #22558066 | 2 |
| C67×#1556 | 2 |
| #9376 | 67 |