Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
1160 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 309 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. C22×C22⋊Dic157 | C2 | semidirect |
| 2. #23757153 | C2 | semidirect |
| 3. #23757136 | C2 | semidirect |
| 4. #23757129 | C2 | semidirect |
| 6. C23×Dic157 | C22 | semidirect |
| 9. C2×C22⋊Dic157 | C22 | semidirect |
| 10. C2×C22⋊Dic157 | C22 | semidirect |
| 11. #19097678 | C22 | semidirect |
| 15. C22×D4×C157 | C4 | semidirect |
| 28. C24×C157 | C2×C4 | semidirect |
| 36. C2×D4×C157 | C2×C4 | semidirect |
| 38. C22×C4×C157 | C2×C4 | semidirect |
| 52. C23×C157 | C22⋊C4 | semidirect |
| 87. C157 | #2308 | semidirect |
| 97. C22×D4 | Dic157 | semidirect |
| 110. C24 | C2×Dic157 | semidirect |
| 118. C2×D4 | C2×Dic157 | semidirect |
| 123. C22×C4 | C2×Dic157 | semidirect |
| 137. C23 | C22⋊Dic157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic157 | 2 |
| #23757153 | 2 |
| #23757136 | 2 |
| #23757129 | 2 |
| C23×D4×C157 | 2 |
| #2308 | 157 |