Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23757997 | C2 | semidirect |
| 3. #23757625 | C2 | semidirect |
| 4. #23757616 | C2 | semidirect |
| 5. #23757515 | C2 | semidirect |
| 6. #23757484 | C2 | semidirect |
| 7. #23757436 | C2 | semidirect |
| 8. C4×#14578942 | C2 | semidirect |
| 9. #23757338 | C2 | semidirect |
| 10. #23757266 | C2 | semidirect |
| 11. #474×C157 | C2 | semidirect |
| 125. C157 | #3302 | semidirect |
| 131. #474 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757997 | 2 |
| #23757927 | 2 |
| #23757625 | 2 |
| #23757616 | 2 |
| #23757515 | 2 |
| #23757484 | 2 |
| #23757436 | 2 |
| C4×#14578942 | 2 |
| #23757338 | 2 |
| #23757266 | 2 |
| #474×C157 | 2 |
| #3302 | 157 |