Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
484 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19097793 | C2 | semidirect |
| 2. #23757851 | C2 | semidirect |
| 3. #23757519 | C2 | semidirect |
| 4. #23757514 | C2 | semidirect |
| 5. #23757509 | C2 | semidirect |
| 6. C2×#19097705 | C2 | semidirect |
| 7. #23757275 | C2 | semidirect |
| 8. C2×#131×C157 | C2 | semidirect |
| 56. C2×C8×C157 | D4 | semidirect |
| 108. C157 | #3061 | semidirect |
| 111. C2×#131 | D157 | semidirect |
| 160. C2×C8 | C22⋊D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097793 | 2 |
| #23757851 | 2 |
| #23757519 | 2 |
| #23757514 | 2 |
| #23757509 | 2 |
| C2×#19097705 | 2 |
| #23757275 | 2 |
| C2×#131×C157 | 2 |
| #3061 | 157 |