Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
232 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 4. C2×C4⋊Dic137 | C4 | semidirect |
| 8. C2×C4×Dic137 | C4 | semidirect |
| 10. #17984003 | C4 | semidirect |
| 14. #99×C137 | C4 | semidirect |
| 103. C137 | #1393 | semidirect |
| 118. #99 | Dic137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984003 | 2 |
| #22577306 | 2 |
| C2×#99×C137 | 2 |
| #1393 | 137 |