Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19097777 | C2 | semidirect |
| 2. #23757847 | C2 | semidirect |
| 4. #23757516 | C2 | semidirect |
| 5. #23757499 | C2 | semidirect |
| 6. #23757311 | C2 | semidirect |
| 7. #23757282 | C2 | semidirect |
| 8. #23757278 | C2 | semidirect |
| 9. C22×SD16×C157 | C2 | semidirect |
| 13. C2×#14578937 | C22 | semidirect |
| 14. C2×C8×D157 | C22 | semidirect |
| 20. #19097747 | C22 | semidirect |
| 25. #19097705 | C22 | semidirect |
| 26. #19097703 | C22 | semidirect |
| 27. #19097695 | C22 | semidirect |
| 68. C2×C8×C157 | D4 | semidirect |
| 120. C157 | #3057 | semidirect |
| 122. C22×SD16 | D157 | semidirect |
| 180. C2×C8 | C22⋊D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097777 | 2 |
| #23757847 | 2 |
| #23757840 | 2 |
| #23757516 | 2 |
| #23757499 | 2 |
| #23757311 | 2 |
| #23757282 | 2 |
| #23757278 | 2 |
| C22×SD16×C157 | 2 |
| #3057 | 157 |