Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#17984887 | C2 | semidirect |
| 2. C2×#17984870 | C2 | semidirect |
| 3. C22×#14555770 | C2 | semidirect |
| 4. #22581522 | C2 | semidirect |
| 5. #22581099 | C2 | semidirect |
| 6. #22581088 | C2 | semidirect |
| 7. #22580947 | C2 | semidirect |
| 8. #22580921 | C2 | semidirect |
| 9. #418×C139 | C2 | semidirect |
| 15. C2×#14555784 | C22 | semidirect |
| 16. C22×D556 | C22 | semidirect |
| 19. C2×D4×D139 | C22 | semidirect |
| 21. C2×#14555774 | C22 | semidirect |
| 22. C2×D1112 | C22 | semidirect |
| 24. C2×#14555770 | C22 | semidirect |
| 25. C22×C139⋊C8 | C22 | semidirect |
| 28. #17984817 | C22 | semidirect |
| 30. #17984765 | C22 | semidirect |
| 31. #17984762 | C22 | semidirect |
| 32. (C2×D139)⋊C8 | C22 | semidirect |
| 34. C2×M16×C139 | C22 | semidirect |
| 35. #117×C139 | C22 | semidirect |
| 36. #102×C139 | C22 | semidirect |
| 42. #14555785 | D4 | semidirect |
| 75. C2×D4×C139 | D4 | semidirect |
| 151. C139 | #3008 | semidirect |
| 159. #418 | D139 | semidirect |
| 178. C2×M16 | C2×D139 | semidirect |
| 184. #117 | C2×D139 | semidirect |
| 187. #102 | C2×D139 | semidirect |
| 218. C2×D4 | D556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984887 | 2 |
| C2×#17984870 | 2 |
| C22×#14555770 | 2 |
| #22581522 | 2 |
| #22581099 | 2 |
| #22581088 | 2 |
| #22580947 | 2 |
| #22580921 | 2 |
| #418×C139 | 2 |
| #3008 | 139 |