Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
648 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 157 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×D1256 | C2 | semidirect |
| 2. C22×#14578939 | C2 | semidirect |
| 3. C2×#19097767 | C2 | semidirect |
| 4. C2×#19097733 | C2 | semidirect |
| 5. #23757467 | C2 | direct (N × H) |
| 6. C2×#19097700 | C2 | semidirect |
| 7. C2×#19097691 | C2 | semidirect |
| 8. C2×#102×C157 | C2 | semidirect |
| 15. C2×D1256 | C22 | semidirect |
| 17. C2×#14578939 | C22 | semidirect |
| 20. #19097767 | C22 | semidirect |
| 22. #19097733 | C22 | semidirect |
| 25. #19097700 | C22 | semidirect |
| 26. #19097691 | C22 | semidirect |
| 30. #102×C157 | C22 | semidirect |
| 38. C2×D628 | D4 | semidirect |
| 80. D628 | C2×D4 | semidirect |
| 84. C2×Dic157 | D8 | semidirect |
| 125. Dic157 | C2×D8 | semidirect |
| 127. C2×C157 | #459 | semidirect |
| 133. C157 | C2×#459 | semidirect |
| 142. C2×#102 | D157 | semidirect |
| 164. #102 | C2×D157 | semidirect |
| 263. C2 | #23757467 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1256 | 2 |
| C22×#14578939 | 2 |
| C2×#19097767 | 2 |
| C2×#19097733 | 2 |
| #23757467 | 2 |
| C2×#19097700 | 2 |
| C2×#19097691 | 2 |
| C2×#102×C157 | 2 |
| C2×#459 | 157 |