Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #23757138 | C2 | semidirect |
| 5. #23757041 | C2 | semidirect |
| 6. #23757032 | C2 | semidirect |
| 7. #428×C157 | C2 | semidirect |
| 17. #19097697 | C4 | semidirect |
| 46. C4×Dic157 | C2×C4 | semidirect |
| 50. M16×C157 | C2×C4 | semidirect |
| 111. C157 | #1860 | semidirect |
| 114. #428 | D157 | semidirect |
| 154. M16 | C4×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757753 | 2 |
| C2×#19097697 | 2 |
| #23757272 | 2 |
| #23757138 | 2 |
| #23757041 | 2 |
| #23757032 | 2 |
| #428×C157 | 2 |
| #1860 | 157 |