Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 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. C2×#19097796 | C2 | semidirect |
| 2. C2×C4×D628 | C2 | semidirect |
| 3. #23757485 | C2 | semidirect |
| 4. #23757475 | C2 | semidirect |
| 5. #23757465 | C2 | semidirect |
| 6. #23757297 | C2 | semidirect |
| 7. #23757274 | C2 | semidirect |
| 8. #532×C157 | C2 | semidirect |
| 21. C4⋊#11929434 | C22 | semidirect |
| 22. C4⋊#11929434 | C22 | semidirect |
| 23. #19097695 | C22 | semidirect |
| 24. #19097692 | C22 | semidirect |
| 26. C4⋊Q8×C157 | C22 | semidirect |
| 27. #127×C157 | C22 | semidirect |
| 28. #124×C157 | C22 | semidirect |
| 37. C2×D628 | D4 | semidirect |
| 119. C4×C157 | AGL(1,ℤ/8) | semidirect |
| 129. C157 | #3036 | semidirect |
| 132. #532 | D157 | semidirect |
| 146. C4⋊Q8 | C2×D157 | semidirect |
| 147. #127 | C2×D157 | semidirect |
| 148. #124 | C2×D157 | semidirect |
| 250. C4 | #19097796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097796 | 2 |
| C2×C4×D628 | 2 |
| #23757485 | 2 |
| #23757475 | 2 |
| #23757465 | 2 |
| #23757297 | 2 |
| #23757274 | 2 |
| #532×C157 | 2 |
| #3036 | 157 |