Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
288 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 133. C67 | #13524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561983 | 2 |
| C2×#16863211 | 2 |
| #22561930 | 2 |
| #22561122 | 2 |
| #22560334 | 2 |
| #22558294 | 2 |
| C67×#2161 | 2 |
| #13524 | 67 |