Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23757988 | C2 | semidirect |
| 2. #23757928 | C2 | semidirect |
| 3. #23757671 | C2 | semidirect |
| 4. #23757596 | C2 | semidirect |
| 5. #23757590 | C2 | semidirect |
| 6. #23757563 | C2 | semidirect |
| 7. #23757553 | C2 | semidirect |
| 8. #23757523 | C2 | semidirect |
| 9. #23757352 | C2 | semidirect |
| 10. #23757314 | C2 | semidirect |
| 11. C4×D8×C157 | C2 | semidirect |
| 101. C8×C157 | #41 | semidirect |
| 127. C157 | #3354 | semidirect |
| 137. C4×D8 | D157 | semidirect |
| 229. C8 | #14578954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757988 | 2 |
| #23757928 | 2 |
| #23757671 | 2 |
| #23757596 | 2 |
| #23757590 | 2 |
| #23757563 | 2 |
| #23757553 | 2 |
| #23757523 | 2 |
| #23757352 | 2 |
| #23757314 | 2 |
| C4×D8×C157 | 2 |
| #3354 | 157 |