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. #22581487 | C2 | semidirect |
| 2. C2×C4×D556 | C2 | semidirect |
| 3. #22581284 | C2 | semidirect |
| 4. #22581267 | C2 | semidirect |
| 5. #22581254 | C2 | semidirect |
| 6. #22581169 | C2 | semidirect |
| 7. #22581106 | C2 | semidirect |
| 9. #22581066 | C2 | semidirect |
| 10. #22581055 | C2 | semidirect |
| 11. #432×C139 | C2 | semidirect |
| 17. #17984834 | C22 | semidirect |
| 18. #17984830 | C22 | semidirect |
| 22. C4×Dic278 | C22 | semidirect |
| 27. C4×D556 | C22 | semidirect |
| 32. #17984776 | C22 | semidirect |
| 33. #17984774 | C22 | semidirect |
| 34. #17984767 | C22 | semidirect |
| 37. #17984764 | C22 | semidirect |
| 39. C4⋊C8×C139 | C22 | semidirect |
| 42. #97×C139 | C22 | semidirect |
| 140. C139 | #3114 | semidirect |
| 152. #432 | D139 | semidirect |
| 176. C4⋊C8 | C2×D139 | semidirect |
| 183. #97 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581487 | 2 |
| C2×C4×D556 | 2 |
| #22581284 | 2 |
| #22581267 | 2 |
| #22581254 | 2 |
| #22581169 | 2 |
| #22581106 | 2 |
| #22581089 | 2 |
| #22581066 | 2 |
| #22581055 | 2 |
| #432×C139 | 2 |
| #3114 | 139 |