Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22578031 | C2 | semidirect |
| 3. #22577766 | C2 | semidirect |
| 4. #22577764 | C2 | semidirect |
| 5. #22577759 | C2 | semidirect |
| 6. #22577748 | C2 | semidirect |
| 7. #22577407 | C2 | semidirect |
| 8. #22577404 | C2 | semidirect |
| 9. C2×#17984010 | C2 | semidirect |
| 10. #22577358 | C2 | semidirect |
| 11. #416×C137 | C2 | semidirect |
| 15. #17984087 | C22 | semidirect |
| 18. #17984079 | C22 | semidirect |
| 26. #17984012 | C22 | semidirect |
| 29. #17984009 | C22 | semidirect |
| 32. #17983998 | C22 | semidirect |
| 33. C8×Dic137 | C22 | semidirect |
| 37. #103×C137 | C22 | semidirect |
| 38. #103×C137 | C22 | semidirect |
| 39. #102×C137 | C22 | semidirect |
| 40. #102×C137 | C22 | semidirect |
| 135. C137 | #3136 | semidirect |
| 145. #416 | D137 | semidirect |
| 166. #103 | C2×D137 | semidirect |
| 167. #103 | C2×D137 | semidirect |
| 173. #102 | C2×D137 | semidirect |
| 174. #102 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578031 | 2 |
| #22577967 | 2 |
| #22577766 | 2 |
| #22577764 | 2 |
| #22577759 | 2 |
| #22577748 | 2 |
| #22577407 | 2 |
| #22577404 | 2 |
| C2×#17984010 | 2 |
| #22577358 | 2 |
| #416×C137 | 2 |
| #3136 | 137 |