Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
488 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 488 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 |
|---|---|---|
| 167. C67 | #10171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570591 | 2 |
| C2×#16863746 | 2 |
| #22561199 | 2 |
| #22558880 | 2 |
| #22558664 | 2 |
| #22558045 | 2 |
| C67×#3209 | 2 |
| #10171 | 67 |