Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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. #23757164 | C2 | semidirect |
| 3. #23757162 | C2 | semidirect |
| 4. #23757131 | C2 | semidirect |
| 6. C4×C22⋊Dic157 | C2 | semidirect |
| 7. C4×C22⋊C4×C157 | C2 | semidirect |
| 10. C2×#14578933 | C22 | semidirect |
| 12. C2×#14578931 | C4 | semidirect |
| 17. C2×C4×Dic157 | C22 | semidirect |
| 18. #19097678 | C22 | semidirect |
| 19. #19097678 | C22 | semidirect |
| 22. C2×C42×C157 | C22 | semidirect |
| 23. #95×C157 | C22 | semidirect |
| 99. C157 | #2312 | semidirect |
| 107. C4×C22⋊C4 | D157 | semidirect |
| 120. C2×C42 | C2×D157 | semidirect |
| 123. #95 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578931 | 2 |
| #23757164 | 2 |
| #23757162 | 2 |
| #23757131 | 2 |
| #23757128 | 2 |
| C4×C22⋊Dic157 | 2 |
| C4×C22⋊C4×C157 | 2 |
| #2312 | 157 |