Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23757901 | C2 | semidirect |
| 3. #23757642 | C2 | semidirect |
| 4. #23757633 | C2 | semidirect |
| 5. #23757628 | C2 | semidirect |
| 6. #23757624 | C2 | semidirect |
| 7. #23757283 | C2 | semidirect |
| 10. C2×#19097696 | C2 | semidirect |
| 11. #405×C157 | C2 | semidirect |
| 127. C157 | #3137 | semidirect |
| 139. #405 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757901 | 2 |
| #23757849 | 2 |
| #23757642 | 2 |
| #23757633 | 2 |
| #23757628 | 2 |
| #23757624 | 2 |
| #23757283 | 2 |
| #23757275 | 2 |
| #23757270 | 2 |
| C2×#19097696 | 2 |
| #405×C157 | 2 |
| #3137 | 157 |