Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23757826 | C2 | semidirect |
| 3. #23757636 | C2 | semidirect |
| 4. #23757618 | C2 | semidirect |
| 5. #23757279 | C2 | semidirect |
| 6. #23757278 | C2 | semidirect |
| 7. #23757277 | C2 | semidirect |
| 8. M16×Dic157 | C2 | semidirect |
| 9. #418×C157 | C2 | semidirect |
| 13. #19097770 | C22 | semidirect |
| 17. #19097762 | C22 | semidirect |
| 22. #19097693 | C22 | semidirect |
| 23. #19097692 | C22 | semidirect |
| 24. #19097691 | C22 | semidirect |
| 25. #19097681 | C22 | semidirect |
| 26. C8×Dic157 | C22 | semidirect |
| 30. #102×C157 | C22 | semidirect |
| 111. C157 | #3138 | semidirect |
| 120. #418 | D157 | semidirect |
| 140. #102 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757826 | 2 |
| C2×#19097767 | 2 |
| #23757636 | 2 |
| #23757618 | 2 |
| #23757279 | 2 |
| #23757278 | 2 |
| #23757277 | 2 |
| M16×Dic157 | 2 |
| #418×C157 | 2 |
| #3138 | 157 |