Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
308 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 308 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 |
|---|---|---|
| 1. #22561983 | C2 | semidirect |
| 5. #22560334 | C2 | semidirect |
| 6. #22558294 | C2 | semidirect |
| 7. C67×#2161 | C2 | semidirect |
| 131. #2161 | D67 | semidirect |
| 138. C67 | #13523 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561983 | 2 |
| C2×#16863208 | 2 |
| #22561926 | 2 |
| #22561117 | 2 |
| #22560334 | 2 |
| #22558294 | 2 |
| C67×#2161 | 2 |
| #13523 | 67 |