Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
292 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. #22562003 | C2 | semidirect |
| 5. #22558321 | C2 | semidirect |
| 6. #22558312 | C2 | semidirect |
| 7. C67×#1388 | C2 | semidirect |
| 140. #1388 | D67 | semidirect |
| 142. C67 | #13498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562003 | 2 |
| #22561819 | 2 |
| #22560244 | 2 |
| #22558321 | 2 |
| #22558312 | 2 |
| C67×#1388 | 2 |
| #13498 | 67 |