Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
338 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 1. Q8×Dic314 | C2 | semidirect |
| 4. #23757624 | C2 | semidirect |
| 6. #23757559 | C2 | semidirect |
| 8. #23757484 | C2 | semidirect |
| 9. #23757381 | C2 | semidirect |
| 11. #446×C157 | C2 | semidirect |
| 116. C157 | #3369 | semidirect |
| 126. #446 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic314 | 2 |
| #23757996 | 2 |
| #23757633 | 2 |
| #23757624 | 2 |
| #23757564 | 2 |
| #23757559 | 2 |
| #23757496 | 2 |
| #23757484 | 2 |
| #23757381 | 2 |
| C4×#14578943 | 2 |
| #446×C157 | 2 |
| #3369 | 157 |