Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
142 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 59 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. #23757380 | C2 | semidirect |
| 3. #23757096 | C2 | semidirect |
| 4. #23757089 | C2 | semidirect |
| 6. #23757050 | C2 | semidirect |
| 18. Q32×C157 | C4 | semidirect |
| 19. SD32×C157 | C4 | semidirect |
| 64. C157 | #2180 | semidirect |
| 77. Q32 | Dic157 | semidirect |
| 78. SD32 | Dic157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757395 | 2 |
| #23757380 | 2 |
| #23757096 | 2 |
| #23757089 | 2 |
| #23757083 | 2 |
| #23757050 | 2 |
| #510×C157 | 2 |
| #2180 | 157 |