Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19097791 | C2 | semidirect |
| 2. #23757928 | C2 | semidirect |
| 3. #23757652 | C2 | semidirect |
| 4. #23757512 | C2 | semidirect |
| 5. #23757478 | C2 | semidirect |
| 6. #23757475 | C2 | semidirect |
| 7. #23757435 | C2 | semidirect |
| 8. #23757433 | C2 | semidirect |
| 9. C4×#14578939 | C2 | semidirect |
| 10. D4×#11929434 | C2 | semidirect |
| 11. #547×C157 | C2 | semidirect |
| 53. #14578939 | D4 | semidirect |
| 127. C4×C157 | #135 | semidirect |
| 138. C157 | #3283 | semidirect |
| 142. #547 | D157 | semidirect |
| 268. C4 | #19097791 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097791 | 2 |
| #23757928 | 2 |
| #23757652 | 2 |
| #23757512 | 2 |
| #23757478 | 2 |
| #23757475 | 2 |
| #23757435 | 2 |
| #23757433 | 2 |
| C4×#14578939 | 2 |
| D4×#11929434 | 2 |
| #547×C157 | 2 |
| #3283 | 157 |