Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
274 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 274 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 |
| 3. #23757291 | C2 | semidirect |
| 4. #23757277 | C2 | semidirect |
| 5. #23757255 | C2 | semidirect |
| 6. C2×#19097687 | C2 | semidirect |
| 7. #344×C157 | C2 | semidirect |
| 110. C157 | #2048 | semidirect |
| 118. #344 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097799 | 2 |
| #23757321 | 2 |
| #23757291 | 2 |
| #23757277 | 2 |
| #23757255 | 2 |
| C2×#19097687 | 2 |
| #344×C157 | 2 |
| #2048 | 157 |