Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 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. C2×C4×D556 | C2 | semidirect |
| 2. #22581281 | C2 | semidirect |
| 3. #22581264 | C2 | semidirect |
| 4. #22581250 | C2 | semidirect |
| 5. #22581165 | C2 | semidirect |
| 6. #22581103 | C2 | semidirect |
| 8. #22581063 | C2 | semidirect |
| 9. #22581051 | C2 | semidirect |
| 10. #22581010 | C2 | semidirect |
| 11. #529×C139 | C2 | semidirect |
| 22. #17984775 | C22 | semidirect |
| 23. #17984773 | C22 | semidirect |
| 24. C4⋊(C139⋊C8) | C22 | semidirect |
| 25. #17984766 | C22 | semidirect |
| 26. #17984763 | C22 | semidirect |
| 31. #17984753 | C22 | semidirect |
| 33. #125×C139 | C22 | semidirect |
| 34. #124×C139 | C22 | semidirect |
| 38. C4×Q8×C139 | C22 | semidirect |
| 40. C4×D4×C139 | C22 | semidirect |
| 140. C139 | #3114 | semidirect |
| 142. #529 | D139 | semidirect |
| 158. #125 | C2×D139 | semidirect |
| 159. #124 | C2×D139 | semidirect |
| 163. C4×Q8 | C2×D139 | semidirect |
| 169. C4×D4 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D556 | 2 |
| #22581281 | 2 |
| #22581264 | 2 |
| #22581250 | 2 |
| #22581165 | 2 |
| #22581103 | 2 |
| #22581086 | 2 |
| #22581063 | 2 |
| #22581051 | 2 |
| #22581010 | 2 |
| #529×C139 | 2 |
| #3114 | 139 |