Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22581588 | C2 | semidirect |
| 3. #22581265 | C2 | semidirect |
| 4. #22581230 | C2 | semidirect |
| 5. #22581188 | C2 | semidirect |
| 6. #22581145 | C2 | semidirect |
| 7. #22581088 | C2 | semidirect |
| 8. C4×D1112 | C2 | semidirect |
| 9. C8×D556 | C2 | semidirect |
| 10. #102×D139 | C2 | semidirect |
| 11. #486×C139 | C2 | semidirect |
| 16. C2×#14555770 | C22 | semidirect |
| 17. C2×C8×D139 | C22 | semidirect |
| 20. #17984817 | C22 | semidirect |
| 26. C4×D556 | C22 | semidirect |
| 27. C4⋊C4×D139 | C22 | semidirect |
| 28. #17984776 | C22 | semidirect |
| 29. #17984775 | C22 | semidirect |
| 30. C4⋊(C139⋊C8) | C22 | semidirect |
| 32. #17984764 | C22 | semidirect |
| 33. #17984763 | C22 | semidirect |
| 35. (C2×D139)⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C139 | C22 | semidirect |
| 38. #102×C139 | C22 | semidirect |
| 39. #102×C139 | C22 | semidirect |
| 40. C4×C8×C139 | C22 | semidirect |
| 88. D556 | D8 | semidirect |
| 89. D556 | #41 | semidirect |
| 142. C139 | #3294 | semidirect |
| 146. #486 | D139 | semidirect |
| 161. C4⋊Q8 | C2×D139 | semidirect |
| 180. #102 | C2×D139 | semidirect |
| 181. #102 | C2×D139 | semidirect |
| 183. C4×C8 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581606 | 2 |
| #22581588 | 2 |
| #22581265 | 2 |
| #22581230 | 2 |
| #22581188 | 2 |
| #22581145 | 2 |
| #22581088 | 2 |
| C4×D1112 | 2 |
| C8×D556 | 2 |
| #102×D139 | 2 |
| #486×C139 | 2 |
| #3294 | 139 |