Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
168 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 5. C4×#11764049 | C4 | semidirect |
| 14. C4×#10587739 | C8 | semidirect |
| 21. C4×Dic137 | C8 | semidirect |
| 22. C42×C137 | C8 | semidirect |
| 56. C137 | #1274 | semidirect |
| 79. C42 | #11764049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578516 | 2 |
| #22578339 | 2 |
| #1274 | 137 |