Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
172 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 172 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. #23757652 | C2 | semidirect |
| 5. #23757025 | C2 | semidirect |
| 6. #23757020 | C2 | semidirect |
| 7. #332×C157 | C2 | semidirect |
| 46. D628 | Q16 | semidirect |
| 78. C157 | #1669 | semidirect |
| 86. #332 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757652 | 2 |
| #23757554 | 2 |
| #23757550 | 2 |
| #23757338 | 2 |
| #23757025 | 2 |
| #23757020 | 2 |
| #332×C157 | 2 |
| #1669 | 157 |