Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic314 | C2 | semidirect |
| 2. #23757625 | C2 | semidirect |
| 3. #23757603 | C2 | semidirect |
| 4. #23757555 | C2 | semidirect |
| 5. #23757500 | C2 | semidirect |
| 6. #23757478 | C2 | semidirect |
| 7. #23757411 | C2 | semidirect |
| 8. C4×#14578942 | C2 | semidirect |
| 9. D4×#11929434 | C2 | semidirect |
| 10. C2×#19097694 | C2 | semidirect |
| 81. Dic314 | #41 | semidirect |
| 95. D4×C157 | SD16 | semidirect |
| 128. C157 | #3298 | semidirect |
| 217. D4 | #14578942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic314 | 2 |
| #23757625 | 2 |
| #23757603 | 2 |
| #23757555 | 2 |
| #23757500 | 2 |
| #23757478 | 2 |
| #23757411 | 2 |
| C4×#14578942 | 2 |
| D4×#11929434 | 2 |
| C2×#19097694 | 2 |
| #547×C157 | 2 |
| #3298 | 157 |