Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23757945 | C2 | semidirect |
| 2. #23757639 | C2 | semidirect |
| 3. #23757621 | C2 | semidirect |
| 4. #23757570 | C2 | semidirect |
| 5. #23757560 | C2 | semidirect |
| 6. #23757468 | C2 | semidirect |
| 7. #23757468 | C2 | semidirect |
| 8. #23757404 | C2 | semidirect |
| 9. #23757383 | C2 | semidirect |
| 10. C4×#14578939 | C2 | semidirect |
| 11. #554×C157 | C2 | semidirect |
| 94. D4×C157 | #41 | semidirect |
| 129. C157 | #3366 | semidirect |
| 131. #554 | D157 | semidirect |
| 218. D4 | #14578955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757945 | 2 |
| #23757639 | 2 |
| #23757621 | 2 |
| #23757570 | 2 |
| #23757560 | 2 |
| #23757468 | 2 |
| #23757404 | 2 |
| #23757383 | 2 |
| C4×#14578939 | 2 |
| #554×C157 | 2 |
| #3366 | 157 |