Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 11. #16863794 | C4 | semidirect |
| 12. #16863747 | C4 | semidirect |
| 178. C67 | #9296 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571355 | 2 |
| #22562928 | 2 |
| #22561190 | 2 |
| #22558880 | 2 |
| #22558774 | 2 |
| #22558068 | 2 |
| C67×#1274 | 2 |
| #9296 | 67 |