Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#17984134 | C2 | semidirect |
| 2. C22×#14555495 | C2 | semidirect |
| 3. #22577970 | C2 | semidirect |
| 4. #22577547 | C2 | semidirect |
| 5. #22577535 | C2 | semidirect |
| 6. #22577409 | C2 | semidirect |
| 7. #22577399 | C2 | semidirect |
| 8. #22577371 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C137 | C2 | semidirect |
| 12. C2×#14555511 | C22 | semidirect |
| 18. C2×D4×D137 | C22 | semidirect |
| 20. C2×#14555495 | C22 | semidirect |
| 21. C22×#11764040 | C22 | semidirect |
| 24. #17984059 | C22 | semidirect |
| 26. #17984047 | C22 | semidirect |
| 27. #17984012 | C22 | semidirect |
| 28. #17984010 | C22 | semidirect |
| 29. #17984009 | C22 | semidirect |
| 30. #17984000 | C22 | semidirect |
| 32. C22×D4×C137 | C22 | semidirect |
| 34. C2×SD16×C137 | C22 | semidirect |
| 35. C2×D8×C137 | C22 | semidirect |
| 36. C2×M16×C137 | C22 | semidirect |
| 50. C2×D548 | D4 | semidirect |
| 69. #41×C137 | D4 | semidirect |
| 151. C137 | #3008 | semidirect |
| 154. C2×AGL(1,ℤ/8) | D137 | semidirect |
| 172. C22×D4 | C2×D137 | semidirect |
| 174. C2×SD16 | C2×D137 | semidirect |
| 177. C2×D8 | C2×D137 | semidirect |
| 178. C2×M16 | C2×D137 | semidirect |
| 198. #41 | C22⋊D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984134 | 2 |
| C22×#14555495 | 2 |
| #22577970 | 2 |
| #22577547 | 2 |
| #22577535 | 2 |
| #22577409 | 2 |
| #22577399 | 2 |
| #22577371 | 2 |
| C2×AGL(1,ℤ/8)×C137 | 2 |
| #3008 | 137 |