Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
310 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #22560328 | C2 | semidirect |
| 5. #22558104 | C2 | semidirect |
| 6. #22558037 | C2 | semidirect |
| 7. C67×#1301 | C2 | semidirect |
| 158. #1301 | D67 | semidirect |
| 160. C67 | #10629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561040 | 2 |
| #22560328 | 2 |
| #22558859 | 2 |
| #22558856 | 2 |
| #22558104 | 2 |
| #22558037 | 2 |
| C67×#1301 | 2 |
| #10629 | 67 |