Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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. #23757944 | C2 | semidirect |
| 3. #23757649 | C2 | semidirect |
| 4. #23757507 | C2 | semidirect |
| 5. #23757473 | C2 | semidirect |
| 6. #23757470 | C2 | semidirect |
| 7. #23757418 | C2 | semidirect |
| 8. #23757416 | C2 | semidirect |
| 9. C4×#14578944 | C2 | semidirect |
| 10. D4×#11929434 | C2 | semidirect |
| 11. #550×C157 | C2 | semidirect |
| 51. #14578944 | D4 | semidirect |
| 131. C4×C157 | #135 | semidirect |
| 142. C157 | #3287 | semidirect |
| 146. #550 | D157 | semidirect |
| 276. 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 |
| #23757944 | 2 |
| #23757649 | 2 |
| #23757507 | 2 |
| #23757473 | 2 |
| #23757470 | 2 |
| #23757418 | 2 |
| #23757416 | 2 |
| C4×#14578944 | 2 |
| D4×#11929434 | 2 |
| #550×C157 | 2 |
| #3287 | 157 |