Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
210 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 49 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. #23758090 | C2 | semidirect |
| 2. #23757711 | C2 | semidirect |
| 3. C2×#19097716 | C2 | semidirect |
| 4. #23757543 | C2 | semidirect |
| 5. #23757090 | C2 | semidirect |
| 6. #23757081 | C2 | semidirect |
| 7. #350×C157 | C2 | semidirect |
| 90. C157 | #2193 | semidirect |
| 98. #350 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758090 | 2 |
| #23757711 | 2 |
| C2×#19097716 | 2 |
| #23757543 | 2 |
| #23757090 | 2 |
| #23757081 | 2 |
| #350×C157 | 2 |
| #2193 | 157 |