Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
204 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23757649 | C2 | semidirect |
| 2. #23757469 | C2 | semidirect |
| 3. #23757465 | C2 | semidirect |
| 4. #23757338 | C2 | semidirect |
| 5. #23757025 | C2 | semidirect |
| 6. #23757016 | C2 | semidirect |
| 7. #331×C157 | C2 | semidirect |
| 52. D628 | D8 | semidirect |
| 58. #11929434 | D8 | semidirect |
| 92. C157 | #1667 | semidirect |
| 100. #331 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757649 | 2 |
| #23757469 | 2 |
| #23757465 | 2 |
| #23757338 | 2 |
| #23757025 | 2 |
| #23757016 | 2 |
| #331×C157 | 2 |
| #1667 | 157 |