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. #23757943 | C2 | semidirect |
| 2. D4×Dic314 | C2 | semidirect |
| 3. #23757619 | C2 | semidirect |
| 4. #23757618 | C2 | semidirect |
| 5. #23757554 | C2 | semidirect |
| 6. #23757551 | C2 | semidirect |
| 7. #23757466 | C2 | semidirect |
| 8. #23757397 | C2 | semidirect |
| 9. D8×Dic157 | C2 | semidirect |
| 10. C4×#14578939 | C2 | semidirect |
| 11. #459×C157 | C2 | semidirect |
| 78. Dic314 | D8 | semidirect |
| 99. D4×C157 | #41 | semidirect |
| 131. C157 | #3358 | semidirect |
| 140. #459 | D157 | semidirect |
| 222. D4 | #14578953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757943 | 2 |
| D4×Dic314 | 2 |
| #23757619 | 2 |
| #23757618 | 2 |
| #23757554 | 2 |
| #23757551 | 2 |
| #23757466 | 2 |
| #23757397 | 2 |
| D8×Dic157 | 2 |
| C4×#14578939 | 2 |
| #459×C157 | 2 |
| #3358 | 157 |