Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
296 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 10. C4×#11929441 | C4 | semidirect |
| 11. C4×#11929441 | C4 | semidirect |
| 16. C4⋊#11929434 | C4 | semidirect |
| 17. #19097700 | C4 | semidirect |
| 18. C4⋊C8×C157 | C4 | semidirect |
| 26. C4⋊#10597845 | C8 | semidirect |
| 44. #11929441 | C4⋊C4 | semidirect |
| 67. C4×C157 | C4×C8 | semidirect |
| 71. Dic157 | C4×C8 | semidirect |
| 79. C157 | C8×C4⋊C4 | semidirect |
| 94. C4⋊C8 | #10597845 | semidirect |
| 151. C4 | C8×#10597845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D157⋊C8 | 2 |
| C2×C8×#10597845 | 2 |
| C4×C4⋊#10597845 | 2 |
| (C2×#10597845)⋊C8 | 2 |
| C4⋊C8×D157 | 2 |
| C8×C4⋊C4 | 157 |