Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23757928 | C2 | semidirect |
| 2. #23757625 | C2 | semidirect |
| 3. #23757614 | C2 | semidirect |
| 4. #23757560 | C2 | semidirect |
| 5. #23757500 | C2 | semidirect |
| 6. #23757478 | C2 | semidirect |
| 7. #23757416 | C2 | semidirect |
| 8. C4×#14578939 | C2 | semidirect |
| 9. D4×#11929434 | C2 | semidirect |
| 10. #23757267 | C2 | semidirect |
| 11. #555×C157 | C2 | semidirect |
| 130. C157 | #3303 | semidirect |
| 132. #555 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757928 | 2 |
| #23757625 | 2 |
| #23757614 | 2 |
| #23757560 | 2 |
| #23757500 | 2 |
| #23757478 | 2 |
| #23757416 | 2 |
| C4×#14578939 | 2 |
| D4×#11929434 | 2 |
| #23757267 | 2 |
| #555×C157 | 2 |
| #3303 | 157 |