Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
390 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 151. C67 | #7693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568591 | 2 |
| #22559958 | 2 |
| #22558034 | 2 |
| #22558031 | 2 |
| C67×#1744 | 2 |
| #7693 | 67 |