Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
392 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 173 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. #23757335 | C2 | semidirect |
| 3. #23757332 | C2 | semidirect |
| 4. #23757296 | C2 | semidirect |
| 6. C4×#14578938 | C2 | semidirect |
| 7. C4×M16×C157 | C2 | semidirect |
| 16. #19097700 | C22 | semidirect |
| 18. #19097682 | C22 | semidirect |
| 19. C4×#11929434 | C22 | semidirect |
| 22. #97×C157 | C22 | semidirect |
| 23. C4×C8×C157 | C22 | semidirect |
| 79. C157 | #2921 | semidirect |
| 87. C4×M16 | D157 | semidirect |
| 101. #97 | C2×D157 | semidirect |
| 103. C4×C8 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097728 | 2 |
| #23757335 | 2 |
| #23757332 | 2 |
| #23757296 | 2 |
| #23757236 | 2 |
| C4×#14578938 | 2 |
| C4×M16×C157 | 2 |
| #2921 | 157 |