Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 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×#19097699 | C2 | semidirect |
| 3. #23757275 | C2 | semidirect |
| 4. #23757274 | C2 | semidirect |
| 5. #23757139 | C2 | semidirect |
| 6. #23757041 | C2 | semidirect |
| 7. C2×#104×C157 | C2 | semidirect |
| 62. C42×C157 | D4 | semidirect |
| 127. C157 | #2040 | semidirect |
| 131. C2×#104 | D157 | semidirect |
| 190. C42 | C22⋊D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757851 | 2 |
| C2×#19097699 | 2 |
| #23757275 | 2 |
| #23757274 | 2 |
| #23757139 | 2 |
| #23757041 | 2 |
| C2×#104×C157 | 2 |
| #2040 | 157 |