Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 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 |
|---|---|---|
| 2. #23757635 | C2 | semidirect |
| 3. #23757630 | C2 | semidirect |
| 4. #23757281 | C2 | semidirect |
| 6. C4×#14578938 | C2 | semidirect |
| 7. #533×C157 | C2 | semidirect |
| 15. #19097694 | C22 | semidirect |
| 17. #19097682 | C22 | semidirect |
| 18. C4×#11929434 | C22 | semidirect |
| 19. C4⋊Q8×C157 | C22 | semidirect |
| 20. #125×C157 | C22 | semidirect |
| 83. C157 | #3140 | semidirect |
| 85. #533 | D157 | semidirect |
| 95. C4⋊Q8 | C2×D157 | semidirect |
| 96. #125 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097759 | 2 |
| #23757635 | 2 |
| #23757630 | 2 |
| #23757281 | 2 |
| #23757277 | 2 |
| C4×#14578938 | 2 |
| #533×C157 | 2 |
| #3140 | 157 |