Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
334 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 9. #16863424 | C4 | semidirect |
| 10. #16863422 | C4 | semidirect |
| 13. M16×Dic67 | C4 | semidirect |
| 14. C2×#14523953 | C4 | semidirect |
| 123. C67 | #12865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568856 | 2 |
| #22560310 | 2 |
| #22558337 | 2 |
| #22558332 | 2 |
| C67×#1391 | 2 |
| #12865 | 67 |