Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
444 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 444 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. #23757830 | C2 | semidirect |
| 2. #23757608 | C2 | semidirect |
| 3. #23757553 | C2 | semidirect |
| 4. #23757478 | C2 | semidirect |
| 6. #23757373 | C2 | semidirect |
| 7. #23757330 | C2 | semidirect |
| 10. #19097771 | C22 | semidirect |
| 11. #19097771 | C22 | semidirect |
| 16. C4×Dic314 | C22 | semidirect |
| 18. #19097704 | C22 | semidirect |
| 19. C4⋊#11929434 | C22 | semidirect |
| 20. #19097694 | C22 | semidirect |
| 23. #19097682 | C22 | semidirect |
| 112. C157 | #3110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757830 | 2 |
| #23757608 | 2 |
| #23757553 | 2 |
| #23757478 | 2 |
| #23757424 | 2 |
| #23757373 | 2 |
| #23757330 | 2 |
| C2×C4×D4×C157 | 2 |
| #3110 | 157 |