Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
216 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 112. C67 | #13545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22560989 | 2 |
| #22558325 | 2 |
| #22558320 | 2 |
| #22558314 | 2 |
| #22558309 | 2 |
| #22558295 | 2 |
| C67×#1833 | 2 |
| #13545 | 67 |