Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
500 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 189 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. C2×#19097779 | C2 | semidirect |
| 3. #23757350 | C2 | semidirect |
| 4. #23757338 | C2 | semidirect |
| 5. #23757241 | C2 | semidirect |
| 6. C2×C4×#11929434 | C2 | semidirect |
| 7. #423×C157 | C2 | semidirect |
| 34. C2×#11929434 | D4 | semidirect |
| 75. C4×C157 | #131 | semidirect |
| 83. C157 | #2931 | semidirect |
| 89. #423 | D157 | semidirect |
| 160. C4 | #19097779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097779 | 2 |
| #23757823 | 2 |
| #23757350 | 2 |
| #23757338 | 2 |
| #23757241 | 2 |
| C2×C4×#11929434 | 2 |
| #423×C157 | 2 |
| #2931 | 157 |