Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
408 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22558983 | C2 | semidirect |
| 4. #22558893 | C2 | semidirect |
| 5. #22558891 | C2 | semidirect |
| 7. C67×#1301 | C2 | semidirect |
| 168. #1301 | D67 | semidirect |
| 169. C67 | #10453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863687 | 2 |
| #22560198 | 2 |
| #22558983 | 2 |
| #22558893 | 2 |
| #22558891 | 2 |
| #22558601 | 2 |
| C67×#1301 | 2 |
| #10453 | 67 |