Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
220 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 220 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 |
|---|---|---|
| 9. #17984159 | C4 | semidirect |
| 10. #17984158 | C4 | semidirect |
| 17. #17984024 | C4 | semidirect |
| 18. #17984023 | C4 | semidirect |
| 19. #108×C137 | C4 | semidirect |
| 70. C137 | #1778 | semidirect |
| 86. #108 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D137⋊#108 | 2 |
| M16×#10587739 | 2 |
| C2×#17984142 | 2 |
| #22578278 | 2 |
| #108×D137 | 2 |
| #1778 | 137 |