Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
380 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 5. #23757556 | C2 | semidirect |
| 6. #23757481 | C2 | semidirect |
| 8. #23757380 | C2 | semidirect |
| 9. #23757377 | C2 | semidirect |
| 127. C157 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757825 | 2 |
| C2×Q8×Dic157 | 2 |
| #23757604 | 2 |
| #23757601 | 2 |
| #23757556 | 2 |
| #23757481 | 2 |
| #23757429 | 2 |
| #23757380 | 2 |
| #23757377 | 2 |
| #23757327 | 2 |
| #451×C157 | 2 |
| #3113 | 157 |