Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
698 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 214. C67 | #9991 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571030 | 2 |
| C2×#16863552 | 2 |
| #22560133 | 2 |
| #22558573 | 2 |
| #22558572 | 2 |
| #22558097 | 2 |
| C2×#451×C67 | 2 |
| #9991 | 67 |