Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
428 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 88 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. #22578404 | C2 | semidirect |
| 2. C2×#17984150 | C2 | semidirect |
| 3. C4×C4⋊#10587739 | C2 | semidirect |
| 15. #17984085 | C4 | semidirect |
| 18. #17984084 | C4 | semidirect |
| 20. #127×C137 | C4 | semidirect |
| 25. C4⋊#10587739 | D4 | semidirect |
| 96. C4×C137 | #102 | semidirect |
| 99. Dic137 | #102 | semidirect |
| 109. C137 | #1982 | semidirect |
| 123. #127 | #10587739 | semidirect |
| 210. C4 | #17984150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578404 | 2 |
| C2×#17984150 | 2 |
| C4×C4⋊#10587739 | 2 |
| #127×D137 | 2 |
| #1982 | 137 |