Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
348 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 125. C67 | #8865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569294 | 2 |
| #22561150 | 2 |
| #22558994 | 2 |
| #22558109 | 2 |
| C67×#1461 | 2 |
| #8865 | 67 |