Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
314 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 4. #22560372 | C2 | semidirect |
| 5. #22558319 | C2 | semidirect |
| 6. #22558290 | C2 | semidirect |
| 7. C67×#1387 | C2 | semidirect |
| 151. #1387 | D67 | semidirect |
| 153. C67 | #13485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561922 | 2 |
| #22561919 | 2 |
| #22561095 | 2 |
| #22560372 | 2 |
| #22558319 | 2 |
| #22558290 | 2 |
| C67×#1387 | 2 |
| #13485 | 67 |