Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
168 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 80 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. #22578294 | C2 | semidirect |
| 4. #22578293 | C2 | semidirect |
| 9. #17984162 | C4 | semidirect |
| 10. #17984161 | C4 | semidirect |
| 16. #17984028 | C4 | semidirect |
| 18. C16×D137 | C4 | semidirect |
| 19. M32×C137 | C4 | semidirect |
| 28. #14555513 | C2×C4 | semidirect |
| 35. #14555485 | C2×C4 | semidirect |
| 37. C16×C137 | C2×C4 | semidirect |
| 67. D137 | #347 | semidirect |
| 68. C137 | C2×#347 | semidirect |
| 82. M32 | #10587739 | semidirect |
| 106. C16 | C2×#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578459 | 2 |
| C2×#17984142 | 2 |
| #22578294 | 2 |
| #22578293 | 2 |
| M32×D137 | 2 |
| C2×#347 | 137 |