Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
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. #22581508 | C2 | semidirect |
| 3. #22581316 | C2 | semidirect |
| 4. #22581301 | C2 | semidirect |
| 5. #22581300 | C2 | semidirect |
| 6. #22581299 | C2 | semidirect |
| 7. #22580956 | C2 | semidirect |
| 8. C4×#14555768 | C2 | semidirect |
| 9. #486×C139 | C2 | semidirect |
| 14. #17984842 | C22 | semidirect |
| 19. #17984833 | C22 | semidirect |
| 26. #17984764 | C22 | semidirect |
| 27. #17984763 | C22 | semidirect |
| 28. #17984762 | C22 | semidirect |
| 29. #17984752 | C22 | semidirect |
| 30. C4×C139⋊C8 | C22 | semidirect |
| 31. C4⋊Q8×C139 | C22 | semidirect |
| 33. #102×C139 | C22 | semidirect |
| 34. C4×C8×C139 | C22 | semidirect |
| 123. C139 | #3138 | semidirect |
| 131. #486 | D139 | semidirect |
| 139. C4⋊Q8 | C2×D139 | semidirect |
| 155. #102 | C2×D139 | semidirect |
| 158. C4×C8 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581508 | 2 |
| #127×D139 | 2 |
| #22581316 | 2 |
| #22581301 | 2 |
| #22581300 | 2 |
| #22581299 | 2 |
| #22580956 | 2 |
| C4×#14555768 | 2 |
| #486×C139 | 2 |
| #3138 | 139 |