Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
326 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 1. #22578374 | C2 | semidirect |
| 2. #22578346 | C2 | semidirect |
| 3. #22578255 | C2 | semidirect |
| 4. #22578254 | C2 | semidirect |
| 8. #17984145 | C22 | semidirect |
| 11. (C2×#10587739)⋊C4 | C22 | semidirect |
| 13. C2×D4×D137 | C4 | semidirect |
| 16. #17984062 | C4 | semidirect |
| 20. C4⋊C4×D137 | C4 | semidirect |
| 22. #121×C137 | C4 | semidirect |
| 121. C137 | #1510 | semidirect |
| 137. #121 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578374 | 2 |
| #22578346 | 2 |
| #22578255 | 2 |
| #22578254 | 2 |
| #121×D137 | 2 |
| #1510 | 137 |