Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 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×#19097792 | C2 | semidirect |
| 2. #23757945 | C2 | semidirect |
| 3. #23757943 | C2 | semidirect |
| 4. #23757649 | C2 | semidirect |
| 5. #23757508 | C2 | semidirect |
| 6. #23757474 | C2 | semidirect |
| 7. #23757419 | C2 | semidirect |
| 8. #23757417 | C2 | semidirect |
| 9. C4×#14578944 | C2 | semidirect |
| 10. #23757338 | C2 | semidirect |
| 11. #460×C157 | C2 | semidirect |
| 58. #14578944 | D4 | semidirect |
| 130. C4×C157 | #135 | semidirect |
| 142. C157 | #3287 | semidirect |
| 150. #460 | D157 | semidirect |
| 276. C4 | #19097792 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097792 | 2 |
| #23757945 | 2 |
| #23757943 | 2 |
| #23757649 | 2 |
| #23757508 | 2 |
| #23757474 | 2 |
| #23757419 | 2 |
| #23757417 | 2 |
| C4×#14578944 | 2 |
| #23757338 | 2 |
| #460×C157 | 2 |
| #3287 | 157 |