Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23757326 | C2 | semidirect |
| 3. #23756996 | C2 | semidirect |
| 4. #431×C157 | C2 | semidirect |
| 24. C2×D628 | C8 | semidirect |
| 89. C157 | #1460 | semidirect |
| 93. #431 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D628 | 2 |
| #23757326 | 2 |
| #23756996 | 2 |
| #431×C157 | 2 |
| #1460 | 157 |