Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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. #23757980 | C2 | semidirect |
| 2. #23757943 | C2 | semidirect |
| 3. #23757636 | C2 | semidirect |
| 4. #23757619 | C2 | semidirect |
| 5. #23757575 | C2 | semidirect |
| 6. #23757564 | C2 | semidirect |
| 7. #23757466 | C2 | semidirect |
| 8. #23757400 | C2 | semidirect |
| 9. #23757385 | C2 | semidirect |
| 10. C4×#14578939 | C2 | semidirect |
| 11. #459×C157 | C2 | semidirect |
| 97. D4×C157 | #41 | semidirect |
| 129. C157 | #3366 | semidirect |
| 138. #459 | D157 | semidirect |
| 218. D4 | #14578953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757980 | 2 |
| #23757943 | 2 |
| #23757636 | 2 |
| #23757619 | 2 |
| #23757575 | 2 |
| #23757564 | 2 |
| #23757466 | 2 |
| #23757400 | 2 |
| #23757385 | 2 |
| C4×#14578939 | 2 |
| #459×C157 | 2 |
| #3366 | 157 |