Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
568 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22558926 | C2 | semidirect |
| 5. #22558721 | C2 | semidirect |
| 6. #22558103 | C2 | semidirect |
| 7. C67×#3165 | C2 | semidirect |
| 186. #3165 | D67 | semidirect |
| 192. C67 | #10102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571208 | 2 |
| #22566321 | 2 |
| #22558926 | 2 |
| #22558806 | 2 |
| #22558721 | 2 |
| #22558103 | 2 |
| C67×#3165 | 2 |
| #10102 | 67 |