Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
452 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 177 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. #23757352 | C2 | semidirect |
| 3. #23757350 | C2 | semidirect |
| 4. #23757326 | C2 | semidirect |
| 5. #23757235 | C2 | semidirect |
| 6. #431×C157 | C2 | semidirect |
| 9. C2×#14578937 | C22 | semidirect |
| 16. C4⋊#11929434 | C22 | semidirect |
| 18. #19097683 | C22 | semidirect |
| 19. C4×#11929434 | C22 | semidirect |
| 21. C4⋊C8×C157 | C22 | semidirect |
| 23. C4×C8×C157 | C22 | semidirect |
| 60. C2×C4×C157 | M16 | semidirect |
| 88. C157 | #2975 | semidirect |
| 94. #431 | D157 | semidirect |
| 107. C4⋊C8 | C2×D157 | semidirect |
| 112. C4×C8 | C2×D157 | semidirect |
| 148. C2×C4 | #14578937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D628 | 2 |
| #23757352 | 2 |
| #23757350 | 2 |
| #23757326 | 2 |
| #23757235 | 2 |
| #431×C157 | 2 |
| #2975 | 157 |