Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
146 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23757390 | C2 | semidirect |
| 3. #23757389 | C2 | semidirect |
| 4. #23757102 | C2 | semidirect |
| 5. #23757081 | C2 | semidirect |
| 6. C16×Dic157 | C2 | semidirect |
| 7. #359×C157 | C2 | semidirect |
| 11. #19097717 | C4 | semidirect |
| 12. #19097715 | C4 | semidirect |
| 13. #19097714 | C4 | semidirect |
| 14. #19097712 | C4 | semidirect |
| 71. C157 | #2178 | semidirect |
| 78. #359 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757703 | 2 |
| #23757390 | 2 |
| #23757389 | 2 |
| #23757102 | 2 |
| #23757081 | 2 |
| C16×Dic157 | 2 |
| #359×C157 | 2 |
| #2178 | 157 |