Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
370 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 50. C2×Q16×C67 | Q8 | semidirect |
| 148. C67 | #13368 | semidirect |
| 170. C2×Q16 | Dic134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570732 | 2 |
| #22561929 | 2 |
| #22561081 | 2 |
| #22558315 | 2 |
| #22558314 | 2 |
| #22558292 | 2 |
| C67×#2141 | 2 |
| #13368 | 67 |