Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 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. #22577958 | C2 | semidirect |
| 3. #22577766 | C2 | semidirect |
| 4. #22577751 | C2 | semidirect |
| 5. #22577750 | C2 | semidirect |
| 6. #22577749 | C2 | semidirect |
| 7. #22577406 | C2 | semidirect |
| 8. C4×#14555493 | C2 | semidirect |
| 9. #486×C137 | C2 | semidirect |
| 14. #17984088 | C22 | semidirect |
| 19. #17984079 | C22 | semidirect |
| 26. #17984010 | C22 | semidirect |
| 27. #17984009 | C22 | semidirect |
| 28. #17984008 | C22 | semidirect |
| 29. #17983998 | C22 | semidirect |
| 30. C4×#11764040 | C22 | semidirect |
| 31. C4⋊Q8×C137 | C22 | semidirect |
| 33. #102×C137 | C22 | semidirect |
| 34. C4×C8×C137 | C22 | semidirect |
| 123. C137 | #3138 | semidirect |
| 131. #486 | D137 | semidirect |
| 139. C4⋊Q8 | C2×D137 | semidirect |
| 155. #102 | C2×D137 | semidirect |
| 158. C4×C8 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577958 | 2 |
| #127×D137 | 2 |
| #22577766 | 2 |
| #22577751 | 2 |
| #22577750 | 2 |
| #22577749 | 2 |
| #22577406 | 2 |
| C4×#14555493 | 2 |
| #486×C137 | 2 |
| #3138 | 137 |