Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
134 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 27 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 |
|---|---|---|
| 17. C4×Dic137 | C8 | semidirect |
| 18. C42×C137 | C8 | semidirect |
| 49. C137 | #1325 | semidirect |
| 68. C42 | #11764049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578489 | 2 |
| #22578349 | 2 |
| #1325 | 137 |