Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
572 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 572 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×#19097792 | C2 | semidirect |
| 2. #23757824 | C2 | semidirect |
| 3. #23757821 | C2 | semidirect |
| 4. #23757654 | C2 | semidirect |
| 5. #23757652 | C2 | semidirect |
| 6. #23757649 | C2 | semidirect |
| 7. #23757646 | C2 | semidirect |
| 8. C4×C8×D157 | C2 | semidirect |
| 9. #492×C157 | C2 | semidirect |
| 47. C8×D157 | D4 | semidirect |
| 91. C4×C157 | #135 | semidirect |
| 101. C157 | #3147 | semidirect |
| 110. #492 | D157 | semidirect |
| 196. C4 | #19097792 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097792 | 2 |
| #23757824 | 2 |
| #23757821 | 2 |
| #23757654 | 2 |
| #23757652 | 2 |
| #23757649 | 2 |
| #23757646 | 2 |
| C4×C8×D157 | 2 |
| #492×C157 | 2 |
| #3147 | 157 |