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×#19097803 | C2 | semidirect |
| 3. C4×Q8×D157 | C2 | semidirect |
| 4. #23757498 | C2 | semidirect |
| 5. #23757497 | C2 | semidirect |
| 6. #23757480 | C2 | semidirect |
| 7. #23757474 | C2 | semidirect |
| 8. #23757473 | C2 | semidirect |
| 9. #23757295 | C2 | semidirect |
| 10. #23757273 | C2 | semidirect |
| 11. #462×C157 | C2 | semidirect |
| 49. Q8×D157 | D4 | semidirect |
| 133. C4×C157 | #137 | semidirect |
| 146. C157 | #3037 | semidirect |
| 154. #462 | D157 | semidirect |
| 285. C4 | #19097803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097803 | 2 |
| #23757824 | 2 |
| C4×Q8×D157 | 2 |
| #23757498 | 2 |
| #23757497 | 2 |
| #23757480 | 2 |
| #23757474 | 2 |
| #23757473 | 2 |
| #23757295 | 2 |
| #23757273 | 2 |
| #462×C157 | 2 |
| #3037 | 157 |