Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19097794 | C2 | semidirect |
| 2. #23757945 | C2 | semidirect |
| 3. #23757926 | C2 | semidirect |
| 4. #23757647 | C2 | semidirect |
| 5. #23757505 | C2 | semidirect |
| 6. #23757469 | C2 | semidirect |
| 7. #23757434 | C2 | semidirect |
| 8. #23757421 | C2 | semidirect |
| 9. C4×#14578941 | C2 | semidirect |
| 10. #23757338 | C2 | semidirect |
| 11. #462×C157 | C2 | semidirect |
| 60. #14578941 | D4 | semidirect |
| 129. C4×C157 | #135 | semidirect |
| 140. C157 | #3284 | semidirect |
| 147. #462 | D157 | semidirect |
| 272. C4 | #19097794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097794 | 2 |
| #23757945 | 2 |
| #23757926 | 2 |
| #23757647 | 2 |
| #23757505 | 2 |
| #23757469 | 2 |
| #23757434 | 2 |
| #23757421 | 2 |
| C4×#14578941 | 2 |
| #23757338 | 2 |
| #462×C157 | 2 |
| #3284 | 157 |