Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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. #23757586 | C2 | semidirect |
| 3. #23757553 | C2 | semidirect |
| 4. #23757468 | C2 | semidirect |
| 5. #23757407 | C2 | semidirect |
| 6. C4×#14578939 | C2 | semidirect |
| 7. #23757326 | C2 | semidirect |
| 8. C2×C4×D4×C157 | C2 | semidirect |
| 11. #19097771 | C22 | semidirect |
| 12. #19097768 | C22 | semidirect |
| 17. C4×D628 | C22 | semidirect |
| 18. #19097704 | C22 | semidirect |
| 19. C4⋊#11929434 | C22 | semidirect |
| 21. #19097691 | C22 | semidirect |
| 23. C4×#11929434 | C22 | semidirect |
| 81. D4×C157 | #41 | semidirect |
| 88. C2×C4×C157 | D8 | semidirect |
| 120. C157 | #3100 | semidirect |
| 123. C2×C4×D4 | D157 | semidirect |
| 199. D4 | #14578954 | semidirect |
| 208. C2×C4 | #14578939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757823 | 2 |
| #23757586 | 2 |
| #23757553 | 2 |
| #23757468 | 2 |
| #23757407 | 2 |
| C4×#14578939 | 2 |
| #23757326 | 2 |
| C2×C4×D4×C157 | 2 |
| #3100 | 157 |