Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
908 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 407 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. #22559965 | C2 | semidirect |
| 8. #16863351 | C4 | semidirect |
| 9. M16×Dic67 | C4 | semidirect |
| 23. #14523953 | C2×C4 | semidirect |
| 24. C8×Dic67 | C2×C4 | semidirect |
| 90. C67 | #20370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568627 | 2 |
| #22559965 | 2 |
| C2×#16863153 | 2 |
| C2×#338×C67 | 2 |
| #20370 | 67 |