Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
278 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 90. C67 | #12897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22558293 | 2 |
| #22558291 | 2 |
| #22558289 | 2 |
| C67×#1726 | 2 |
| #12897 | 67 |