Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D157 | C2 | semidirect |
| 4. #23757484 | C2 | semidirect |
| 5. #23757482 | C2 | semidirect |
| 6. #23757480 | C2 | semidirect |
| 7. #23757478 | C2 | semidirect |
| 8. #23757476 | C2 | semidirect |
| 9. #23757295 | C2 | semidirect |
| 10. #23757280 | C2 | semidirect |
| 11. #461×C157 | C2 | semidirect |
| 131. C4×C157 | #137 | semidirect |
| 139. Dic157 | #137 | semidirect |
| 145. C157 | #3039 | semidirect |
| 155. #461 | D157 | semidirect |
| 283. C4 | #19097800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097800 | 2 |
| C4⋊Q8×D157 | 2 |
| C4×#14578953 | 2 |
| #23757484 | 2 |
| #23757482 | 2 |
| #23757480 | 2 |
| #23757478 | 2 |
| #23757476 | 2 |
| #23757295 | 2 |
| #23757280 | 2 |
| #461×C157 | 2 |
| #3039 | 157 |