Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
560 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 161 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. C2×#19097730 | C2 | semidirect |
| 3. #23757213 | C2 | semidirect |
| 4. #23757210 | C2 | semidirect |
| 5. #23757205 | C2 | semidirect |
| 6. #23757200 | C2 | semidirect |
| 7. #23757198 | C2 | semidirect |
| 9. C4×C4⋊Dic157 | C2 | semidirect |
| 10. C4×#14578931 | C2 | semidirect |
| 11. C4×C22⋊C4×C157 | C2 | semidirect |
| 137. C157 | #2395 | semidirect |
| 149. C4×C22⋊C4 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D157 | 2 |
| C2×#19097730 | 2 |
| #23757213 | 2 |
| #23757210 | 2 |
| #23757205 | 2 |
| #23757200 | 2 |
| #23757198 | 2 |
| #23757189 | 2 |
| C4×C4⋊Dic157 | 2 |
| C4×#14578931 | 2 |
| C4×C22⋊C4×C157 | 2 |
| #2395 | 157 |