Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
168 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23757558 | C2 | semidirect |
| 4. #23757026 | C2 | semidirect |
| 5. #23757020 | C2 | semidirect |
| 7. #446×C157 | C2 | semidirect |
| 62. C8×C157 | SD16 | semidirect |
| 79. C157 | #1686 | semidirect |
| 84. #446 | D157 | semidirect |
| 142. C8 | #14578941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757646 | 2 |
| #23757558 | 2 |
| #23757473 | 2 |
| #23757026 | 2 |
| #23757020 | 2 |
| #23757016 | 2 |
| #446×C157 | 2 |
| #1686 | 157 |