Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 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. C4×#14578954 | C2 | semidirect |
| 2. #23757594 | C2 | semidirect |
| 3. #23757555 | C2 | semidirect |
| 4. #23757550 | C2 | semidirect |
| 5. #23757470 | C2 | semidirect |
| 6. #23757465 | C2 | semidirect |
| 7. #23757416 | C2 | semidirect |
| 8. #23757383 | C2 | semidirect |
| 9. #23757373 | C2 | semidirect |
| 10. #23757330 | C2 | semidirect |
| 11. #532×C157 | C2 | semidirect |
| 85. Dic314 | #41 | semidirect |
| 87. D628 | #41 | semidirect |
| 144. C157 | #3115 | semidirect |
| 146. #532 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14578954 | 2 |
| #23757594 | 2 |
| #23757555 | 2 |
| #23757550 | 2 |
| #23757470 | 2 |
| #23757465 | 2 |
| #23757416 | 2 |
| #23757383 | 2 |
| #23757373 | 2 |
| #23757330 | 2 |
| #532×C157 | 2 |
| #3115 | 157 |