Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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×#17984135 | C2 | semidirect |
| 2. C22×#14555498 | C2 | semidirect |
| 3. #22577970 | C2 | semidirect |
| 4. #22577545 | C2 | semidirect |
| 5. #22577540 | C2 | semidirect |
| 6. #22577413 | C2 | semidirect |
| 7. #22577399 | C2 | semidirect |
| 8. #22577371 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C137 | C2 | semidirect |
| 15. C2×#14555509 | C22 | semidirect |
| 18. C2×Q8×D137 | C22 | semidirect |
| 27. #17984013 | C22 | semidirect |
| 28. #17984012 | C22 | semidirect |
| 29. #17984009 | C22 | semidirect |
| 30. #17984000 | C22 | semidirect |
| 48. C2×Dic274 | D4 | semidirect |
| 69. #41×C137 | D4 | semidirect |
| 145. C137 | #3010 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D137 | semidirect |
| 191. #41 | C22⋊D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984135 | 2 |
| C22×#14555498 | 2 |
| #22577970 | 2 |
| #22577545 | 2 |
| #22577540 | 2 |
| #22577413 | 2 |
| #22577399 | 2 |
| #22577371 | 2 |
| C2×AGL(1,ℤ/8)×C137 | 2 |
| #3010 | 137 |