Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×Q16×D157 | C2 | semidirect |
| 4. #23757532 | C2 | semidirect |
| 5. #23757531 | C2 | semidirect |
| 6. #23757528 | C2 | semidirect |
| 7. #23757513 | C2 | semidirect |
| 8. #23757512 | C2 | semidirect |
| 9. #23757308 | C2 | semidirect |
| 10. #23757280 | C2 | semidirect |
| 11. #470×C157 | C2 | semidirect |
| 133. C157 | #3059 | semidirect |
| 141. #470 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D157 | 2 |
| C2×#19097779 | 2 |
| #23757846 | 2 |
| #23757532 | 2 |
| #23757531 | 2 |
| #23757528 | 2 |
| #23757513 | 2 |
| #23757512 | 2 |
| #23757308 | 2 |
| #23757280 | 2 |
| #470×C157 | 2 |
| #3059 | 157 |