Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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×#19097778 | C2 | semidirect |
| 2. #23757395 | C2 | semidirect |
| 3. #23757390 | C2 | semidirect |
| 4. #23757322 | C2 | semidirect |
| 5. #23757290 | C2 | semidirect |
| 6. #23757231 | C2 | semidirect |
| 10. #19097778 | C22 | semidirect |
| 11. #19097778 | C22 | semidirect |
| 17. #19097707 | C22 | semidirect |
| 18. #19097698 | C22 | semidirect |
| 19. #19097681 | C22 | semidirect |
| 20. C8×Dic157 | C22 | semidirect |
| 22. #137×C157 | C4 | semidirect |
| 23. AGL(1,ℤ/8)×C157 | C4 | semidirect |
| 89. C157 | #2955 | semidirect |
| 99. #137 | Dic157 | semidirect |
| 100. AGL(1,ℤ/8) | Dic157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097778 | 2 |
| #23757395 | 2 |
| #23757390 | 2 |
| #23757322 | 2 |
| #23757290 | 2 |
| #23757231 | 2 |
| #575×C157 | 2 |
| #2955 | 157 |