Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#19097802 | C2 | semidirect |
| 3. #23757847 | C2 | semidirect |
| 4. #23757434 | C2 | semidirect |
| 5. #23757427 | C2 | semidirect |
| 6. #23757282 | C2 | semidirect |
| 7. #23757270 | C2 | semidirect |
| 8. #23757239 | C2 | semidirect |
| 9. C22×Q16×C157 | C2 | semidirect |
| 140. C157 | #3011 | semidirect |
| 144. C22×Q16 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097819 | 2 |
| C2×#19097802 | 2 |
| #23757847 | 2 |
| #23757434 | 2 |
| #23757427 | 2 |
| #23757282 | 2 |
| #23757270 | 2 |
| #23757239 | 2 |
| C22×Q16×C157 | 2 |
| #3011 | 157 |