Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
520 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 157 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×#19097793 | C2 | semidirect |
| 2. #23757784 | C2 | semidirect |
| 3. #23757514 | C2 | semidirect |
| 4. #23757509 | C2 | semidirect |
| 5. #23757502 | C2 | semidirect |
| 6. #23757311 | C2 | semidirect |
| 7. #23757270 | C2 | semidirect |
| 8. C23×C8×C157 | C2 | semidirect |
| 11. C2×Dic628 | C22 | semidirect |
| 12. C2×#14578943 | C22 | semidirect |
| 13. C2×D1256 | C22 | semidirect |
| 20. #19097705 | C22 | semidirect |
| 21. #19097703 | C22 | semidirect |
| 22. #19097696 | C22 | semidirect |
| 23. #19097693 | C22 | semidirect |
| 56. C2×C8×C157 | D4 | semidirect |
| 91. C22×C157 | #135 | semidirect |
| 106. C157 | #3050 | semidirect |
| 109. C23×C8 | D157 | semidirect |
| 157. C2×C8 | C22⋊D157 | semidirect |
| 200. C22 | #19097793 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097793 | 2 |
| #23757784 | 2 |
| #23757514 | 2 |
| #23757509 | 2 |
| #23757502 | 2 |
| #23757311 | 2 |
| #23757270 | 2 |
| C23×C8×C157 | 2 |
| #3050 | 157 |