Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23758008 | C2 | semidirect |
| 2. #23757945 | C2 | semidirect |
| 3. #23757662 | C2 | semidirect |
| 4. #23757650 | C2 | semidirect |
| 5. #23757489 | C2 | semidirect |
| 6. #23757474 | C2 | semidirect |
| 7. #23757469 | C2 | semidirect |
| 8. #23757469 | C2 | semidirect |
| 9. #23757386 | C2 | semidirect |
| 10. C4×#14578943 | C2 | semidirect |
| 11. #446×C157 | C2 | semidirect |
| 108. C8×C157 | #41 | semidirect |
| 134. C157 | #3399 | semidirect |
| 144. #446 | D157 | semidirect |
| 243. C8 | #14578955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758008 | 2 |
| #23757945 | 2 |
| #23757662 | 2 |
| #23757650 | 2 |
| #23757489 | 2 |
| #23757474 | 2 |
| #23757469 | 2 |
| #23757386 | 2 |
| C4×#14578943 | 2 |
| #446×C157 | 2 |
| #3399 | 157 |