Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
572 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#19097794 | C2 | semidirect |
| 2. C2×#19097792 | C2 | semidirect |
| 3. C2×#19097790 | C2 | semidirect |
| 4. #23757822 | C2 | semidirect |
| 5. #23757657 | C2 | semidirect |
| 6. #23757655 | C2 | semidirect |
| 7. #23757651 | C2 | semidirect |
| 8. #23757648 | C2 | semidirect |
| 9. #23757644 | C2 | semidirect |
| 10. C4×C8×D157 | C2 | semidirect |
| 11. #495×C157 | C2 | semidirect |
| 62. C8×D157 | D4 | semidirect |
| 63. C8×D157 | D4 | semidirect |
| 119. Dic157 | #135 | semidirect |
| 125. C157 | #3147 | semidirect |
| 133. #495 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097794 | 2 |
| C2×#19097792 | 2 |
| C2×#19097790 | 2 |
| #23757822 | 2 |
| #23757657 | 2 |
| #23757655 | 2 |
| #23757651 | 2 |
| #23757648 | 2 |
| #23757644 | 2 |
| C4×C8×D157 | 2 |
| #495×C157 | 2 |
| #3147 | 157 |