Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
356 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23757995 | C2 | semidirect |
| 2. #23757666 | C2 | semidirect |
| 4. #23757495 | C2 | semidirect |
| 6. #23757482 | C2 | semidirect |
| 7. #23757403 | C2 | semidirect |
| 8. #23757372 | C2 | semidirect |
| 9. C4×Q16×C157 | C2 | semidirect |
| 102. C157 | #3402 | semidirect |
| 112. C4×Q16 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757995 | 2 |
| #23757666 | 2 |
| #23757657 | 2 |
| #23757495 | 2 |
| #23757491 | 2 |
| #23757482 | 2 |
| #23757403 | 2 |
| #23757372 | 2 |
| C4×Q16×C157 | 2 |
| #3402 | 157 |