Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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. #23757168 | C2 | semidirect |
| 3. #23757167 | C2 | semidirect |
| 4. #23757161 | C2 | semidirect |
| 5. #23757157 | C2 | semidirect |
| 7. #23757145 | C2 | semidirect |
| 8. #23757131 | C2 | semidirect |
| 12. #19097752 | C4 | semidirect |
| 36. C22×Dic157 | C2×C4 | semidirect |
| 44. #14578933 | C2×C4 | semidirect |
| 48. C22⋊Dic157 | C2×C4 | semidirect |
| 126. C157 | #2376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097752 | 2 |
| #23757168 | 2 |
| #23757167 | 2 |
| #23757161 | 2 |
| #23757157 | 2 |
| #23757153 | 2 |
| #23757145 | 2 |
| #23757131 | 2 |
| #390×C157 | 2 |
| #2376 | 157 |