Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22581663 | C2 | semidirect |
| 3. #22581299 | C2 | semidirect |
| 4. #22581270 | C2 | semidirect |
| 5. #22581244 | C2 | semidirect |
| 6. #22581179 | C2 | semidirect |
| 7. #22581102 | C2 | semidirect |
| 8. C4×#14555772 | C2 | semidirect |
| 9. #22581018 | C2 | semidirect |
| 10. #102×D139 | C2 | semidirect |
| 11. #460×C139 | C2 | semidirect |
| 15. C2×C8×D139 | C22 | semidirect |
| 16. #17984842 | C22 | semidirect |
| 19. #17984818 | C22 | semidirect |
| 26. C4⋊C4×D139 | C22 | semidirect |
| 27. #17984774 | C22 | semidirect |
| 28. #17984773 | C22 | semidirect |
| 29. #17984766 | C22 | semidirect |
| 31. #17984763 | C22 | semidirect |
| 32. #17984763 | C22 | semidirect |
| 34. (C2×D139)⋊C8 | C22 | semidirect |
| 35. C4×C139⋊C8 | C22 | semidirect |
| 36. C2×SD16×C139 | C22 | semidirect |
| 38. C4×Q8×C139 | C22 | semidirect |
| 39. C4⋊C8×C139 | C22 | semidirect |
| 40. #102×C139 | C22 | semidirect |
| 84. D556 | SD16 | semidirect |
| 136. C139 | #3295 | semidirect |
| 144. #460 | D139 | semidirect |
| 152. C2×SD16 | C2×D139 | semidirect |
| 162. C4×Q8 | C2×D139 | semidirect |
| 169. C4⋊C8 | C2×D139 | semidirect |
| 175. #102 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581663 | 2 |
| #22581588 | 2 |
| #22581299 | 2 |
| #22581270 | 2 |
| #22581244 | 2 |
| #22581179 | 2 |
| #22581102 | 2 |
| C4×#14555772 | 2 |
| #22581018 | 2 |
| #102×D139 | 2 |
| #460×C139 | 2 |
| #3295 | 139 |