Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 269 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. #23757146 | C2 | semidirect |
| 4. #23757145 | C2 | semidirect |
| 5. #23757131 | C2 | semidirect |
| 9. C2×#14578933 | C22 | semidirect |
| 11. C2×C22⋊Dic157 | C4 | semidirect |
| 16. #19097678 | C22 | semidirect |
| 25. C22×Dic157 | C2×C4 | semidirect |
| 31. C22⋊Dic157 | C2×C4 | semidirect |
| 32. C22⋊Dic157 | C2×C4 | semidirect |
| 57. C23×C157 | C4⋊C4 | semidirect |
| 98. C157 | #2315 | semidirect |
| 150. C23 | #14578933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic157 | 2 |
| #23757146 | 2 |
| #23757145 | 2 |
| #23757131 | 2 |
| C22×C22⋊C4×C157 | 2 |
| #2315 | 157 |