Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
760 conjugacy classes of subgroups; only the 418 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 418 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. C2×C8×#10587739 | C2 | direct (N × H) |
| 6. C2×#14555518 | C4 | semidirect |
| 8. C22×#11764047 | C4 | semidirect |
| 11. C8×#10587739 | C22 | direct (N × H) |
| 13. C22×#11764040 | C4 | semidirect |
| 14. C2×C8×D137 | C4 | semidirect |
| 16. C22×C8×C137 | C4 | semidirect |
| 17. C22×#10587739 | C8 | direct (N × H) |
| 19. #14555518 | C2×C4 | semidirect |
| 21. C2×#11764047 | C2×C4 | semidirect |
| 30. C2×#11764040 | C2×C4 | semidirect |
| 31. C8×D137 | C2×C4 | semidirect |
| 34. C2×C8×C137 | C2×C4 | semidirect |
| 35. C2×#10587739 | C2×C8 | direct (N × H) |
| 37. #11764047 | C22×C4 | semidirect |
| 48. #11764040 | C22×C4 | semidirect |
| 52. C8×C137 | C22×C4 | semidirect |
| 53. C22×C137 | C4×C8 | semidirect |
| 55. C2×D137 | C4×C8 | semidirect |
| 59. #10587739 | C22×C8 | direct (N × H) |
| 64. C2×C137 | C2×C4×C8 | semidirect |
| 66. D137 | C2×C4×C8 | semidirect |
| 68. C137 | C22×C4×C8 | semidirect |
| 82. C22×C8 | #10587739 | direct (N × H) |
| 101. C2×C8 | C2×#10587739 | direct (N × H) |
| 121. C8 | C22×#10587739 | direct (N × H) |
| 126. C22 | C8×#10587739 | direct (N × H) |
| 135. C2 | C2×C8×#10587739 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555518 | 2 |
| C22×C4×#10587739 | 2 |
| C2×C8×#10587739 | 2 |
| C22×C8×D137 | 2 |
| C22×C4×C8 | 137 |