Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #23757623 | C2 | semidirect |
| 3. #23757606 | C2 | semidirect |
| 4. #23757568 | C2 | semidirect |
| 5. #23757512 | C2 | semidirect |
| 6. #23757480 | C2 | semidirect |
| 7. #23757429 | C2 | semidirect |
| 8. C4×#14578944 | C2 | semidirect |
| 10. C2×#19097695 | C2 | semidirect |
| 92. D4×C157 | Q16 | semidirect |
| 122. C157 | #3299 | semidirect |
| 208. D4 | #14578944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757980 | 2 |
| #23757623 | 2 |
| #23757606 | 2 |
| #23757568 | 2 |
| #23757512 | 2 |
| #23757480 | 2 |
| #23757429 | 2 |
| C4×#14578944 | 2 |
| D4×#11929434 | 2 |
| C2×#19097695 | 2 |
| D4×Q8×C157 | 2 |
| #3299 | 157 |