Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#19097802 | C2 | semidirect |
| 3. #23757433 | C2 | semidirect |
| 4. #23757428 | C2 | semidirect |
| 5. #23757423 | C2 | semidirect |
| 6. #23757272 | C2 | semidirect |
| 7. #23757237 | C2 | semidirect |
| 8. C2×C22⋊Q8×C157 | C2 | semidirect |
| 19. C2×#14578944 | C22 | semidirect |
| 20. C2×#14578941 | C22 | semidirect |
| 21. C2×#14578938 | C22 | semidirect |
| 22. #19097694 | C22 | semidirect |
| 23. #19097691 | C22 | semidirect |
| 25. C22⋊#11929434 | C22 | semidirect |
| 26. C22×Q8×C157 | C22 | semidirect |
| 31. C22⋊Q8×C157 | C22 | semidirect |
| 33. C2×C4⋊C4×C157 | C22 | semidirect |
| 126. C22×C157 | #137 | semidirect |
| 146. C157 | #3007 | semidirect |
| 150. C2×C22⋊Q8 | D157 | semidirect |
| 162. C22×Q8 | C2×D157 | semidirect |
| 174. C22⋊Q8 | C2×D157 | semidirect |
| 176. C2×C4⋊C4 | C2×D157 | semidirect |
| 277. C22 | #19097802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578954 | 2 |
| C2×#19097802 | 2 |
| #23757433 | 2 |
| #23757428 | 2 |
| #23757423 | 2 |
| #23757272 | 2 |
| #23757237 | 2 |
| C2×C22⋊Q8×C157 | 2 |
| #3007 | 157 |