Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 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 |
|---|---|---|
| 3. #23757751 | C2 | semidirect |
| 4. #23757497 | C2 | semidirect |
| 5. #23757481 | C2 | semidirect |
| 6. #23757299 | C2 | semidirect |
| 7. #23757282 | C2 | semidirect |
| 9. C22×Q16×C157 | C2 | semidirect |
| 111. C157 | #3044 | semidirect |
| 114. C22×Q16 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097802 | 2 |
| #23757847 | 2 |
| #23757751 | 2 |
| #23757497 | 2 |
| #23757481 | 2 |
| #23757299 | 2 |
| #23757282 | 2 |
| #23757270 | 2 |
| C22×Q16×C157 | 2 |
| #3044 | 157 |