Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 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 |
|---|---|---|
| 2. #23757177 | C2 | semidirect |
| 3. #23757164 | C2 | semidirect |
| 4. #23757162 | C2 | semidirect |
| 6. C4×#14578931 | C2 | semidirect |
| 7. #23757120 | C2 | semidirect |
| 8. #23757119 | C2 | semidirect |
| 9. #376×C157 | C2 | semidirect |
| 13. #19097759 | C4 | semidirect |
| 35. C2×Dic314 | C2×C4 | semidirect |
| 49. #14578931 | C2×C4 | semidirect |
| 50. #14578931 | C2×C4 | semidirect |
| 59. C42×C157 | C2×C4 | semidirect |
| 119. C157 | #2372 | semidirect |
| 129. #376 | D157 | semidirect |
| 179. C42 | C4×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097759 | 2 |
| #23757177 | 2 |
| #23757164 | 2 |
| #23757162 | 2 |
| #23757151 | 2 |
| C4×#14578931 | 2 |
| #23757120 | 2 |
| #23757119 | 2 |
| #376×C157 | 2 |
| #2372 | 157 |