Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
264 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 7. C22⋊#11764047 | C4 | semidirect |
| 12. C22⋊#11764040 | C4 | semidirect |
| 14. C22⋊C8×C137 | C4 | semidirect |
| 19. C22×#10587739 | C8 | semidirect |
| 88. C137 | #1280 | semidirect |
| 101. C22⋊C8 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578371 | 2 |
| C2×(C2×#10587739)⋊C4 | 2 |
| C22⋊C8×D137 | 2 |
| #1280 | 137 |