Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 3. #23757624 | C2 | semidirect |
| 4. #23757609 | C2 | semidirect |
| 5. #23757569 | C2 | semidirect |
| 6. #23757514 | C2 | semidirect |
| 7. #23757484 | C2 | semidirect |
| 8. #23757431 | C2 | semidirect |
| 9. C4×Dic628 | C2 | semidirect |
| 10. C2×#19097696 | C2 | semidirect |
| 93. D4×C157 | Q16 | semidirect |
| 122. C157 | #3299 | semidirect |
| 208. D4 | Dic628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757980 | 2 |
| D4×Dic314 | 2 |
| #23757624 | 2 |
| #23757609 | 2 |
| #23757569 | 2 |
| #23757514 | 2 |
| #23757484 | 2 |
| #23757431 | 2 |
| C4×Dic628 | 2 |
| C2×#19097696 | 2 |
| C8×D4×C157 | 2 |
| #3299 | 157 |