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. #22581608 | C2 | semidirect |
| 2. #22581588 | C2 | semidirect |
| 3. #22581299 | C2 | semidirect |
| 4. #22581265 | C2 | semidirect |
| 5. #22581234 | C2 | semidirect |
| 6. #22581186 | C2 | semidirect |
| 7. #22581085 | C2 | semidirect |
| 8. C4×#14555770 | C2 | semidirect |
| 9. #22581018 | C2 | semidirect |
| 10. #102×D139 | C2 | semidirect |
| 11. #459×C139 | C2 | semidirect |
| 16. C2×C8×D139 | C22 | semidirect |
| 17. #17984842 | C22 | semidirect |
| 22. #17984813 | C22 | semidirect |
| 26. C4⋊C4×D139 | C22 | semidirect |
| 27. #17984776 | C22 | semidirect |
| 28. #17984775 | C22 | semidirect |
| 30. #17984763 | C22 | semidirect |
| 31. #17984763 | C22 | semidirect |
| 32. #17984763 | C22 | semidirect |
| 34. (C2×D139)⋊C8 | C22 | semidirect |
| 35. C4×C139⋊C8 | C22 | semidirect |
| 36. C2×D8×C139 | C22 | semidirect |
| 38. C4×D4×C139 | C22 | semidirect |
| 39. C4⋊C8×C139 | C22 | semidirect |
| 40. #102×C139 | C22 | semidirect |
| 85. D556 | D8 | semidirect |
| 86. D556 | #41 | semidirect |
| 142. C139 | #3294 | semidirect |
| 150. #459 | D139 | semidirect |
| 159. C2×D8 | C2×D139 | semidirect |
| 171. C4×D4 | C2×D139 | semidirect |
| 175. C4⋊C8 | C2×D139 | semidirect |
| 181. #102 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581608 | 2 |
| #22581588 | 2 |
| #22581299 | 2 |
| #22581265 | 2 |
| #22581234 | 2 |
| #22581186 | 2 |
| #22581085 | 2 |
| C4×#14555770 | 2 |
| #22581018 | 2 |
| #102×D139 | 2 |
| #459×C139 | 2 |
| #3294 | 139 |