Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 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. #22581606 | C2 | semidirect |
| 2. D4×D556 | C2 | semidirect |
| 3. #22581301 | C2 | semidirect |
| 4. #22581268 | C2 | semidirect |
| 5. #22581190 | C2 | semidirect |
| 6. #22581149 | C2 | semidirect |
| 7. #22581088 | C2 | semidirect |
| 8. C4×#14555770 | C2 | semidirect |
| 9. #22581018 | C2 | semidirect |
| 10. #102×D139 | C2 | semidirect |
| 11. #474×C139 | C2 | semidirect |
| 15. C2×D1112 | C22 | semidirect |
| 17. C2×C8×D139 | C22 | semidirect |
| 22. #17984817 | C22 | semidirect |
| 26. C4×D556 | C22 | semidirect |
| 27. C4⋊C4×D139 | C22 | semidirect |
| 28. #17984775 | C22 | semidirect |
| 29. #17984764 | C22 | semidirect |
| 31. #17984762 | 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. #107×C139 | C22 | semidirect |
| 39. C4⋊C8×C139 | C22 | semidirect |
| 92. D556 | D8 | semidirect |
| 105. D4×C139 | #41 | semidirect |
| 142. C139 | #3294 | semidirect |
| 148. #474 | D139 | semidirect |
| 161. C4⋊Q8 | C2×D139 | semidirect |
| 174. #107 | C2×D139 | semidirect |
| 175. C4⋊C8 | C2×D139 | semidirect |
| 240. D4 | #14555786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581606 | 2 |
| D4×D556 | 2 |
| #22581301 | 2 |
| #22581268 | 2 |
| #22581190 | 2 |
| #22581149 | 2 |
| #22581088 | 2 |
| C4×#14555770 | 2 |
| #22581018 | 2 |
| #102×D139 | 2 |
| #474×C139 | 2 |
| #3294 | 139 |