Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 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. #23757944 | C2 | semidirect |
| 2. D4×Dic314 | C2 | semidirect |
| 3. #23757620 | C2 | semidirect |
| 4. #23757618 | C2 | semidirect |
| 5. #23757553 | C2 | semidirect |
| 6. #23757552 | C2 | semidirect |
| 7. #23757468 | C2 | semidirect |
| 8. #23757466 | C2 | semidirect |
| 9. C8×Dic314 | C2 | semidirect |
| 10. #23757353 | C2 | semidirect |
| 11. C4×D8×C157 | C2 | semidirect |
| 78. Dic314 | D8 | semidirect |
| 96. D4×C157 | #41 | semidirect |
| 131. C157 | #3358 | semidirect |
| 143. C4×D8 | D157 | semidirect |
| 222. D4 | #14578954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757944 | 2 |
| D4×Dic314 | 2 |
| #23757620 | 2 |
| #23757618 | 2 |
| #23757553 | 2 |
| #23757552 | 2 |
| #23757468 | 2 |
| #23757466 | 2 |
| C8×Dic314 | 2 |
| #23757353 | 2 |
| C4×D8×C157 | 2 |
| #3358 | 157 |