Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
188 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 11. #16863236 | C4 | semidirect |
| 89. C67 | #13653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863236 | 2 |
| Q32×Dic67 | 2 |
| #22562067 | 2 |
| #22558410 | 2 |
| #22558391 | 2 |
| #22558342 | 2 |
| C67×#1416 | 2 |
| #13653 | 67 |