Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 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. #23757173 | C2 | semidirect |
| 3. #23757163 | C2 | semidirect |
| 4. #23757158 | C2 | semidirect |
| 5. #23757151 | C2 | semidirect |
| 6. #23757149 | C2 | semidirect |
| 7. #23757144 | C2 | semidirect |
| 8. #23757136 | C2 | semidirect |
| 9. #380×C157 | C2 | semidirect |
| 13. #19097745 | C4 | semidirect |
| 37. C2×C22⋊D157 | C2×C4 | semidirect |
| 44. C4⋊Dic157 | C2×C4 | semidirect |
| 50. #14578931 | C2×C4 | semidirect |
| 54. C22×C4×C157 | C2×C4 | semidirect |
| 129. C157 | #2377 | semidirect |
| 139. #380 | D157 | semidirect |
| 176. C22×C4 | C4×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097745 | 2 |
| #23757173 | 2 |
| #23757163 | 2 |
| #23757158 | 2 |
| #23757151 | 2 |
| #23757149 | 2 |
| #23757144 | 2 |
| #23757136 | 2 |
| #380×C157 | 2 |
| #2377 | 157 |