Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
448 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 448 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. #22578276 | C2 | semidirect |
| 7. D137⋊M16 | C4 | semidirect |
| 11. #17984167 | C4 | semidirect |
| 17. C2×C4⋊Dic137 | C4 | semidirect |
| 21. C4⋊C4×D137 | C4 | semidirect |
| 23. C2×C4⋊C4×C137 | C4 | semidirect |
| 28. #14555518 | C2×C4 | semidirect |
| 31. C4⋊#10587739 | C2×C4 | semidirect |
| 120. C137 | #1736 | semidirect |
| 142. C2×C4⋊C4 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D137⋊M16 | 2 |
| C2×#17984167 | 2 |
| #22578276 | 2 |
| C2×C4⋊C4×D137 | 2 |
| #1736 | 137 |