Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
446 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 10. #16863688 | C4 | semidirect |
| 11. #16863678 | C4 | semidirect |
| 186. C67 | #9178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570010 | 2 |
| #22563172 | 2 |
| #22558773 | 2 |
| #22558603 | 2 |
| #22558112 | 2 |
| #22558068 | 2 |
| C67×#1503 | 2 |
| #9178 | 67 |