Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
272 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 13. #19097838 | C4 | semidirect |
| 14. C4⋊#11929441 | C4 | semidirect |
| 21. #19097682 | C4 | semidirect |
| 22. #19097681 | C4 | semidirect |
| 23. #19097681 | C4 | semidirect |
| 24. #97×C157 | C4 | semidirect |
| 72. #11929434 | C4⋊C4 | semidirect |
| 77. C8×C157 | C4⋊C4 | semidirect |
| 98. C157 | #1771 | semidirect |
| 121. #97 | #10597845 | semidirect |
| 176. C8 | C4⋊#10597845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D157⋊(C4⋊C8) | 2 |
| C2×#19097825 | 2 |
| C2×C8×#10597845 | 2 |
| C4×C4⋊#10597845 | 2 |
| (C2×#10597845)⋊C8 | 2 |
| #97×D157 | 2 |
| #1771 | 157 |