Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 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. #22581664 | C2 | semidirect |
| 3. #22581301 | C2 | semidirect |
| 4. #22581273 | C2 | semidirect |
| 5. #22581183 | C2 | semidirect |
| 6. #22581154 | C2 | semidirect |
| 7. #22581105 | C2 | semidirect |
| 8. C4×#14555773 | C2 | semidirect |
| 9. #22581018 | C2 | semidirect |
| 10. #102×D139 | C2 | semidirect |
| 11. #476×C139 | C2 | semidirect |
| 14. C2×#14555774 | C22 | semidirect |
| 16. C2×C8×D139 | C22 | semidirect |
| 19. #17984822 | C22 | semidirect |
| 24. C4×Dic278 | C22 | semidirect |
| 27. C4⋊C4×D139 | C22 | semidirect |
| 28. #17984773 | C22 | semidirect |
| 29. #17984765 | C22 | semidirect |
| 30. #17984764 | C22 | semidirect |
| 32. #17984762 | C22 | semidirect |
| 33. #17984762 | C22 | semidirect |
| 34. (C2×D139)⋊C8 | C22 | semidirect |
| 35. C4×C139⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C139 | C22 | semidirect |
| 38. #106×C139 | C22 | semidirect |
| 39. C4⋊C8×C139 | C22 | semidirect |
| 89. D556 | SD16 | semidirect |
| 136. C139 | #3295 | semidirect |
| 142. #476 | D139 | semidirect |
| 154. C4⋊Q8 | C2×D139 | semidirect |
| 168. #106 | C2×D139 | semidirect |
| 169. C4⋊C8 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581664 | 2 |
| D4×D556 | 2 |
| #22581301 | 2 |
| #22581273 | 2 |
| #22581183 | 2 |
| #22581154 | 2 |
| #22581105 | 2 |
| C4×#14555773 | 2 |
| #22581018 | 2 |
| #102×D139 | 2 |
| #476×C139 | 2 |
| #3295 | 139 |