Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14578944 | C2 | semidirect |
| 4. C2×#19097736 | C2 | semidirect |
| 5. #23757498 | C2 | direct (N × H) |
| 6. C2×#19097700 | C2 | semidirect |
| 8. C2×#103×C157 | C2 | semidirect |
| 12. C2×#14578944 | C22 | semidirect |
| 19. #19097736 | C22 | semidirect |
| 25. #19097700 | C22 | semidirect |
| 30. #103×C157 | C22 | semidirect |
| 110. C2×C157 | #464 | semidirect |
| 115. C157 | C2×#464 | semidirect |
| 123. C2×#103 | D157 | semidirect |
| 145. #103 | C2×D157 | semidirect |
| 227. C2 | #23757498 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578944 | 2 |
| C22×#14578943 | 2 |
| C2×#19097760 | 2 |
| C2×#19097736 | 2 |
| #23757498 | 2 |
| C2×#19097700 | 2 |
| C2×#19097691 | 2 |
| C2×#103×C157 | 2 |
| C2×#464 | 157 |