Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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. C22×#14555785 | C2 | semidirect |
| 2. C2×#17984868 | C2 | semidirect |
| 3. #22581096 | C2 | semidirect |
| 4. #22581091 | C2 | semidirect |
| 5. #22581086 | C2 | semidirect |
| 6. #22580952 | C2 | semidirect |
| 7. #22580917 | C2 | semidirect |
| 8. C2×#121×C139 | C2 | semidirect |
| 13. C2×#14555785 | C22 | semidirect |
| 14. C22×Dic278 | C22 | semidirect |
| 15. C22×D556 | C22 | semidirect |
| 19. C2×#14555773 | C22 | semidirect |
| 20. C2×#14555770 | C22 | semidirect |
| 21. C2×#14555769 | C22 | semidirect |
| 22. #17984765 | C22 | semidirect |
| 23. #17984762 | C22 | semidirect |
| 24. C22⋊(C139⋊C8) | C22 | semidirect |
| 25. C22⋊(C139⋊C8) | C22 | semidirect |
| 27. C22×D4×C139 | C22 | semidirect |
| 32. #121×C139 | C22 | semidirect |
| 33. C2×C4⋊C4×C139 | C22 | semidirect |
| 41. #14555785 | D4 | semidirect |
| 85. Dic278 | C2×D4 | semidirect |
| 88. D556 | C2×D4 | semidirect |
| 135. C22×C139 | AGL(1,ℤ/8) | semidirect |
| 155. C139 | #3006 | semidirect |
| 159. C2×#121 | D139 | semidirect |
| 174. C22×D4 | C2×D139 | semidirect |
| 184. #121 | C2×D139 | semidirect |
| 185. C2×C4⋊C4 | C2×D139 | semidirect |
| 295. C22 | #17984868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555785 | 2 |
| C2×#17984868 | 2 |
| #22581096 | 2 |
| #22581091 | 2 |
| #22581086 | 2 |
| #22580952 | 2 |
| #22580917 | 2 |
| C2×#121×C139 | 2 |
| #3006 | 139 |