Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
306 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 144. C67 | #10610 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561198 | 2 |
| #22560984 | 2 |
| #22558980 | 2 |
| #22558893 | 2 |
| C2×#16863143 | 2 |
| #22558084 | 2 |
| C67×#1565 | 2 |
| #10610 | 67 |