Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
296 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 126 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. #17984155 | C4 | semidirect |
| 10. C4⋊#11764047 | C4 | semidirect |
| 16. C4×#11764040 | C4 | semidirect |
| 17. C8×Dic137 | C4 | semidirect |
| 18. C8×Dic137 | C4 | semidirect |
| 19. C4×C8×C137 | C4 | semidirect |
| 24. C4⋊#10587739 | C8 | direct (N × H) |
| 57. #11764040 | C4⋊C4 | semidirect |
| 62. C8×C137 | C4⋊C4 | semidirect |
| 70. C4×C137 | C4×C8 | semidirect |
| 74. Dic137 | C4×C8 | semidirect |
| 82. C137 | C8×C4⋊C4 | semidirect |
| 101. C4×C8 | #10587739 | semidirect |
| 145. C8 | C4⋊#10587739 | direct (N × H) |
| 157. C4 | C8×#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578404 | 2 |
| C2×C8×#10587739 | 2 |
| C4×C4⋊#10587739 | 2 |
| #22578268 | 2 |
| C4×C8×D137 | 2 |
| C8×C4⋊C4 | 137 |