Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
416 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 3. #22578268 | C2 | semidirect |
| 7. C2×#14555518 | C4 | semidirect |
| 9. C22×#11764047 | C4 | semidirect |
| 16. C2×#14555494 | C4 | semidirect |
| 17. C2×#14555493 | C4 | semidirect |
| 21. C2×M16×C137 | C4 | semidirect |
| 102. C137 | #1729 | semidirect |
| 113. C2×M16 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555518 | 2 |
| C2×#17984167 | 2 |
| #22578268 | 2 |
| C2×M16×D137 | 2 |
| #1729 | 137 |