Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
408 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 2. C2×#16863219 | C2 | semidirect |
| 4. #22558318 | C2 | semidirect |
| 17. #349×C67 | C4 | semidirect |
| 131. C67 | #12931 | semidirect |
| 142. #349 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863445 | 2 |
| C2×#16863219 | 2 |
| #22560242 | 2 |
| #22558318 | 2 |
| C2×#349×C67 | 2 |
| #12931 | 67 |