Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
316 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 316 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 |
|---|---|---|
| 126. C67 | #10668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561191 | 2 |
| #22560362 | 2 |
| #22558984 | 2 |
| #22558983 | 2 |
| #22558612 | 2 |
| #22558037 | 2 |
| C67×#1481 | 2 |
| #10668 | 67 |