Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 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×#14578943 | C2 | semidirect |
| 2. C22×#14578942 | C2 | semidirect |
| 4. C2×#19097736 | C2 | semidirect |
| 5. #23757472 | C2 | direct (N × H) |
| 6. C2×#19097700 | C2 | semidirect |
| 7. C2×#19097691 | C2 | semidirect |
| 8. C2×#102×C157 | C2 | semidirect |
| 14. C2×#14578943 | C22 | semidirect |
| 16. C2×#14578942 | C22 | semidirect |
| 21. #19097736 | C22 | semidirect |
| 25. #19097700 | C22 | semidirect |
| 26. #19097691 | C22 | semidirect |
| 30. #102×C157 | C22 | semidirect |
| 34. C2×Dic314 | D4 | semidirect |
| 72. Dic314 | C2×D4 | semidirect |
| 81. C2×Dic157 | SD16 | semidirect |
| 118. Dic157 | C2×SD16 | semidirect |
| 120. C2×C157 | #460 | semidirect |
| 125. C157 | C2×#460 | semidirect |
| 134. C2×#102 | D157 | semidirect |
| 156. #102 | C2×D157 | semidirect |
| 247. C2 | #23757472 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578943 | 2 |
| C22×#14578942 | 2 |
| C2×#19097767 | 2 |
| C2×#19097736 | 2 |
| #23757472 | 2 |
| C2×#19097700 | 2 |
| C2×#19097691 | 2 |
| C2×#102×C157 | 2 |
| C2×#460 | 157 |