Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. C2×Q8×Dic157 | C2 | semidirect |
| 3. #23757587 | C2 | semidirect |
| 4. #23757584 | C2 | semidirect |
| 5. #23757566 | C2 | semidirect |
| 6. #23757471 | C2 | semidirect |
| 7. #23757412 | C2 | semidirect |
| 8. #23757376 | C2 | semidirect |
| 9. #23757374 | C2 | semidirect |
| 10. #23757327 | C2 | semidirect |
| 11. #448×C157 | C2 | semidirect |
| 104. Q8×C157 | #41 | semidirect |
| 140. C157 | #3112 | semidirect |
| 149. #448 | D157 | semidirect |
| 229. Q8 | #14578953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757818 | 2 |
| C2×Q8×Dic157 | 2 |
| #23757587 | 2 |
| #23757584 | 2 |
| #23757566 | 2 |
| #23757471 | 2 |
| #23757412 | 2 |
| #23757376 | 2 |
| #23757374 | 2 |
| #23757327 | 2 |
| #448×C157 | 2 |
| #3112 | 157 |