Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
572 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 157 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×#19097791 | C2 | semidirect |
| 2. #23757823 | C2 | semidirect |
| 3. #23757655 | C2 | semidirect |
| 4. #23757652 | C2 | semidirect |
| 5. #23757649 | C2 | semidirect |
| 6. #23757647 | C2 | semidirect |
| 7. #23757645 | C2 | semidirect |
| 8. C2×C4×#11929434 | C2 | semidirect |
| 9. #532×C157 | C2 | semidirect |
| 42. C2×#11929434 | D4 | semidirect |
| 93. C4×C157 | #135 | semidirect |
| 101. C157 | #3147 | semidirect |
| 105. #532 | D157 | semidirect |
| 196. C4 | #19097791 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097791 | 2 |
| #23757823 | 2 |
| #23757655 | 2 |
| #23757652 | 2 |
| #23757649 | 2 |
| #23757647 | 2 |
| #23757645 | 2 |
| C2×C4×#11929434 | 2 |
| #532×C157 | 2 |
| #3147 | 157 |