Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
422 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 205 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. #23757345 | C2 | semidirect |
| 2. D4×#11929434 | C2 | semidirect |
| 3. #23757334 | C2 | semidirect |
| 4. #23757240 | C2 | semidirect |
| 5. C2×C22⋊#11929434 | C2 | semidirect |
| 7. C2×#14578938 | C22 | semidirect |
| 9. C22×#11929434 | C22 | semidirect |
| 10. C4⋊#11929434 | C22 | semidirect |
| 14. C22⋊#11929434 | C22 | semidirect |
| 15. #19097682 | C22 | semidirect |
| 16. C4×#11929434 | C22 | semidirect |
| 89. C157 | #2977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757345 | 2 |
| D4×#11929434 | 2 |
| #23757334 | 2 |
| #23757240 | 2 |
| C2×C22⋊#11929434 | 2 |
| #525×C157 | 2 |
| #2977 | 157 |