Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
408 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23757823 | C2 | semidirect |
| 2. #23757807 | C2 | semidirect |
| 3. #23757682 | C2 | semidirect |
| 4. #23757662 | C2 | semidirect |
| 5. #23757638 | C2 | semidirect |
| 6. #23757633 | C2 | semidirect |
| 7. #23757526 | C2 | semidirect |
| 8. #23757519 | C2 | semidirect |
| 9. C4×#14578943 | C2 | semidirect |
| 10. C4×D1256 | C2 | semidirect |
| 11. C4×M16×C157 | C2 | semidirect |
| 110. C8×C157 | #41 | semidirect |
| 137. C157 | #3171 | semidirect |
| 149. C4×M16 | D157 | semidirect |
| 248. C8 | #14578954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757823 | 2 |
| #23757807 | 2 |
| #23757682 | 2 |
| #23757662 | 2 |
| #23757638 | 2 |
| #23757633 | 2 |
| #23757526 | 2 |
| #23757519 | 2 |
| C4×#14578943 | 2 |
| C4×D1256 | 2 |
| C4×M16×C157 | 2 |
| #3171 | 157 |