Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 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. #135×D139 | C2 | semidirect |
| 2. #22581395 | C2 | semidirect |
| 3. #22581392 | C2 | semidirect |
| 4. #22581390 | C2 | semidirect |
| 5. #22581387 | C2 | semidirect |
| 6. #22581385 | C2 | semidirect |
| 7. #22581383 | C2 | semidirect |
| 8. C2×#17984781 | C2 | semidirect |
| 9. #508×C139 | C2 | semidirect |
| 12. #17984864 | C22 | semidirect |
| 16. Q16×D139 | C22 | semidirect |
| 18. D8×D139 | C22 | semidirect |
| 20. Dic1112 | C22 | semidirect |
| 21. #17984788 | C22 | semidirect |
| 22. #17984787 | C22 | semidirect |
| 23. #17984786 | C22 | semidirect |
| 24. #17984785 | C22 | semidirect |
| 25. D2224 | C22 | semidirect |
| 26. #17984783 | C22 | semidirect |
| 27. #17984781 | C22 | semidirect |
| 28. #17984781 | C22 | semidirect |
| 29. C2×C139⋊C16 | C22 | semidirect |
| 30. #135×C139 | C22 | semidirect |
| 31. Q32×C139 | C22 | semidirect |
| 32. SD32×C139 | C22 | semidirect |
| 33. D16×C139 | C22 | semidirect |
| 34. C2×C16×C139 | C22 | semidirect |
| 103. C139 | #3414 | semidirect |
| 112. #508 | D139 | semidirect |
| 120. #135 | C2×D139 | semidirect |
| 127. Q32 | C2×D139 | semidirect |
| 131. SD32 | C2×D139 | semidirect |
| 134. D16 | C2×D139 | semidirect |
| 138. C2×C16 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D139 | 2 |
| #22581395 | 2 |
| #22581392 | 2 |
| #22581390 | 2 |
| #22581387 | 2 |
| #22581385 | 2 |
| #22581383 | 2 |
| C2×#17984781 | 2 |
| #508×C139 | 2 |
| #3414 | 139 |