Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #22580853 | C2 | semidirect |
| 3. #22580847 | C2 | semidirect |
| 4. #22580841 | C2 | semidirect |
| 5. #22580829 | C2 | semidirect |
| 6. #22580809 | C2 | semidirect |
| 7. #379×C139 | C2 | semidirect |
| 9. C22×C4×D139 | C22 | semidirect |
| 10. #17984811 | C4 | semidirect |
| 11. C2×Dic139⋊C4 | C22 | semidirect |
| 15. C2×(C2×D139)⋊C4 | C22 | semidirect |
| 16. C2×C4×Dic139 | C22 | semidirect |
| 17. C139⋊#95 | C22 | semidirect |
| 18. C139⋊#95 | C22 | semidirect |
| 33. C22⋊Dic139 | C2×C4 | semidirect |
| 38. C24×C139 | C2×C4 | semidirect |
| 95. C139 | #2375 | semidirect |
| 103. #379 | D139 | semidirect |
| 121. C24 | C4×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984811 | 2 |
| #22580853 | 2 |
| #22580847 | 2 |
| #22580841 | 2 |
| #22580829 | 2 |
| #22580809 | 2 |
| #379×C139 | 2 |
| #2375 | 139 |