Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
254 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. #23757321 | C2 | semidirect |
| 4. #23757281 | C2 | semidirect |
| 6. C2×#19097689 | C2 | semidirect |
| 7. #344×C157 | C2 | semidirect |
| 105. C157 | #2049 | semidirect |
| 113. #344 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097804 | 2 |
| #23757321 | 2 |
| #23757291 | 2 |
| #23757281 | 2 |
| #23757255 | 2 |
| C2×#19097689 | 2 |
| #344×C157 | 2 |
| #2049 | 157 |