Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
872 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 233 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×#19097736 | C2 | semidirect |
| 3. #23757174 | C2 | semidirect |
| 4. #23757173 | C2 | semidirect |
| 5. #23757132 | C2 | semidirect |
| 6. C4×C22⋊Dic157 | C2 | semidirect |
| 7. #23757120 | C2 | semidirect |
| 8. #380×C157 | C2 | semidirect |
| 10. C2×#14578954 | C4 | semidirect |
| 60. Dic314 | C22⋊C4 | semidirect |
| 70. C2×Dic157 | #41 | semidirect |
| 114. C157 | #2341 | semidirect |
| 121. #380 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578954 | 2 |
| C2×#19097736 | 2 |
| #23757174 | 2 |
| #23757173 | 2 |
| #23757132 | 2 |
| C4×C22⋊Dic157 | 2 |
| #23757120 | 2 |
| #380×C157 | 2 |
| #2341 | 157 |