Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23757756 | C2 | semidirect |
| 2. #23757611 | C2 | semidirect |
| 3. #23757606 | C2 | semidirect |
| 4. #23757594 | C2 | semidirect |
| 5. #23757584 | C2 | semidirect |
| 6. #23757313 | C2 | semidirect |
| 7. C2×#19097704 | C2 | semidirect |
| 8. #23757274 | C2 | semidirect |
| 9. #23757269 | C2 | semidirect |
| 10. #23757240 | C2 | semidirect |
| 133. C157 | #3098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757756 | 2 |
| #23757611 | 2 |
| #23757606 | 2 |
| #23757594 | 2 |
| #23757584 | 2 |
| #23757313 | 2 |
| C2×#19097704 | 2 |
| #23757274 | 2 |
| #23757269 | 2 |
| #23757240 | 2 |
| #537×C157 | 2 |
| #3098 | 157 |