Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 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. #23757927 | C2 | semidirect |
| 3. #23757926 | C2 | semidirect |
| 4. #23757652 | C2 | semidirect |
| 5. #23757513 | C2 | semidirect |
| 6. #23757479 | C2 | semidirect |
| 7. #23757438 | C2 | semidirect |
| 8. #23757432 | C2 | semidirect |
| 9. C4×#14578939 | C2 | semidirect |
| 10. #23757338 | C2 | semidirect |
| 11. #461×C157 | C2 | semidirect |
| 58. #14578939 | D4 | semidirect |
| 126. C4×C157 | #135 | semidirect |
| 138. C157 | #3283 | semidirect |
| 146. #461 | D157 | semidirect |
| 268. 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 |
| #23757927 | 2 |
| #23757926 | 2 |
| #23757652 | 2 |
| #23757513 | 2 |
| #23757479 | 2 |
| #23757438 | 2 |
| #23757432 | 2 |
| C4×#14578939 | 2 |
| #23757338 | 2 |
| #461×C157 | 2 |
| #3283 | 157 |