Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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×#14578954 | C2 | semidirect |
| 2. C2×#19097799 | C2 | semidirect |
| 3. C2×#19097745 | C2 | semidirect |
| 4. #23757420 | C2 | semidirect |
| 5. #23757414 | C2 | semidirect |
| 6. #23757409 | C2 | semidirect |
| 7. #23757275 | C2 | semidirect |
| 8. #407×C157 | C2 | semidirect |
| 13. C2×#14578954 | C22 | semidirect |
| 14. C22×Dic314 | C22 | semidirect |
| 15. C22×D628 | C22 | semidirect |
| 16. C22×D628 | C22 | semidirect |
| 21. C2×#14578943 | C22 | semidirect |
| 22. C2×D1256 | C22 | semidirect |
| 26. #19097745 | C22 | semidirect |
| 27. C2×C4⋊Dic157 | C22 | semidirect |
| 29. #19097696 | C22 | semidirect |
| 30. #19097693 | C22 | semidirect |
| 32. C2×M16×C157 | C22 | semidirect |
| 33. C22⋊C8×C157 | C22 | semidirect |
| 34. C22⋊C8×C157 | C22 | semidirect |
| 42. #14578954 | D4 | semidirect |
| 89. Dic314 | C2×D4 | semidirect |
| 94. D628 | C2×D4 | semidirect |
| 131. C22×C157 | AGL(1,ℤ/8) | semidirect |
| 155. C157 | #3006 | semidirect |
| 164. #407 | D157 | semidirect |
| 180. C2×M16 | C2×D157 | semidirect |
| 189. C22⋊C8 | C2×D157 | semidirect |
| 190. C22⋊C8 | C2×D157 | semidirect |
| 295. C22 | #19097799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578954 | 2 |
| C2×#19097799 | 2 |
| C2×#19097745 | 2 |
| #23757420 | 2 |
| #23757414 | 2 |
| #23757409 | 2 |
| #23757275 | 2 |
| #407×C157 | 2 |
| #3006 | 157 |