Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
158 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 158 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 |
|---|---|---|
| 33. C32×C67 | Q8 | semidirect |
| 83. C67 | #13660 | semidirect |
| 109. C32 | Dic134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×Dic134 | 2 |
| C4⋊(C67⋊C32) | 2 |
| Dic67⋊C32 | 2 |
| #22558342 | 2 |
| C32×Dic67 | 2 |
| C67×#1397 | 2 |
| #13660 | 67 |