Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
412 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22561197 | C2 | semidirect |
| 4. #22558934 | C2 | semidirect |
| 6. #22558082 | C2 | semidirect |
| 7. C67×#1307 | C2 | semidirect |
| 187. #1307 | D67 | semidirect |
| 189. C67 | #9337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571238 | 2 |
| #22569376 | 2 |
| #22561197 | 2 |
| #22558934 | 2 |
| #22558817 | 2 |
| #22558082 | 2 |
| C67×#1307 | 2 |
| #9337 | 67 |