Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
242 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 61 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. #23757649 | C2 | semidirect |
| 2. #23757649 | C2 | semidirect |
| 3. #23757645 | C2 | semidirect |
| 4. #23757620 | C2 | semidirect |
| 5. #23757619 | C2 | semidirect |
| 6. #23756995 | C2 | semidirect |
| 7. #493×C157 | C2 | semidirect |
| 48. #11929434 | D8 | semidirect |
| 81. C157 | #1721 | semidirect |
| 85. #493 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757649 | 2 |
| #23757645 | 2 |
| #23757620 | 2 |
| #23757619 | 2 |
| #23756995 | 2 |
| #493×C157 | 2 |
| #1721 | 157 |