Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. C22×#14555495 | C2 | semidirect |
| 2. #22577967 | C2 | semidirect |
| 3. #22577878 | C2 | semidirect |
| 4. #22577620 | C2 | semidirect |
| 5. #22577596 | C2 | semidirect |
| 6. #22577431 | C2 | semidirect |
| 7. #22577409 | C2 | semidirect |
| 8. #22577399 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C137 | C2 | semidirect |
| 14. #17984084 | C22 | semidirect |
| 15. #17984077 | C22 | semidirect |
| 19. D4×Dic137 | C22 | semidirect |
| 23. #17984017 | C22 | semidirect |
| 24. #17984012 | C22 | semidirect |
| 25. #17984010 | C22 | semidirect |
| 26. #17984009 | C22 | semidirect |
| 30. C2×SD16×C137 | C22 | semidirect |
| 31. C2×D8×C137 | C22 | semidirect |
| 58. C2×D4×C137 | D4 | semidirect |
| 121. C137 | #3041 | semidirect |
| 123. C2×AGL(1,ℤ/8) | D137 | semidirect |
| 136. C2×SD16 | C2×D137 | semidirect |
| 139. C2×D8 | C2×D137 | semidirect |
| 168. C2×D4 | C22⋊D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555495 | 2 |
| #22577967 | 2 |
| #22577878 | 2 |
| #22577620 | 2 |
| #22577596 | 2 |
| #22577431 | 2 |
| #22577409 | 2 |
| #22577399 | 2 |
| C2×AGL(1,ℤ/8)×C137 | 2 |
| #3041 | 137 |