Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 137 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×#17984872 | C2 | semidirect |
| 2. C2×#17984872 | C2 | semidirect |
| 3. #22581720 | C2 | semidirect |
| 4. #22581226 | C2 | semidirect |
| 5. #22581214 | C2 | semidirect |
| 6. #22581001 | C2 | semidirect |
| 7. #22580937 | C2 | semidirect |
| 8. C2×#17984760 | C2 | semidirect |
| 16. C2×#14555775 | C22 | semidirect |
| 18. C2×#14555773 | C22 | semidirect |
| 25. #17984777 | C22 | semidirect |
| 26. #17984761 | C22 | semidirect |
| 27. #17984760 | C22 | semidirect |
| 28. #17984759 | C22 | semidirect |
| 142. C139 | #3069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984872 | 2 |
| #22581720 | 2 |
| #22581226 | 2 |
| #22581214 | 2 |
| #22581001 | 2 |
| #22580937 | 2 |
| C2×#17984760 | 2 |
| #575×C139 | 2 |
| #3069 | 139 |