Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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×#19097800 | C2 | semidirect |
| 3. C4×Q8×D157 | C2 | semidirect |
| 4. #23757494 | C2 | semidirect |
| 5. #23757493 | C2 | semidirect |
| 6. #23757484 | C2 | semidirect |
| 7. #23757483 | C2 | semidirect |
| 8. #23757470 | C2 | semidirect |
| 9. #23757295 | C2 | semidirect |
| 10. #23757271 | C2 | semidirect |
| 11. #460×C157 | C2 | semidirect |
| 50. Q8×D157 | D4 | semidirect |
| 132. C4×C157 | #137 | semidirect |
| 146. C157 | #3037 | semidirect |
| 156. #460 | D157 | semidirect |
| 285. 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 |
| #23757821 | 2 |
| C4×Q8×D157 | 2 |
| #23757494 | 2 |
| #23757493 | 2 |
| #23757484 | 2 |
| #23757483 | 2 |
| #23757470 | 2 |
| #23757295 | 2 |
| #23757271 | 2 |
| #460×C157 | 2 |
| #3037 | 157 |