Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
360 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 85 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×#19097700 | C2 | semidirect |
| 3. C2×#19097693 | C2 | semidirect |
| 4. #23757176 | C2 | semidirect |
| 5. #23757174 | C2 | semidirect |
| 6. #23757035 | C2 | semidirect |
| 7. C2×#102×C157 | C2 | semidirect |
| 80. C2×Dic157 | D8 | semidirect |
| 142. C157 | #2054 | semidirect |
| 147. C2×#102 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578939 | 2 |
| C2×#19097700 | 2 |
| C2×#19097693 | 2 |
| #23757176 | 2 |
| #23757174 | 2 |
| #23757035 | 2 |
| C2×#102×C157 | 2 |
| #2054 | 157 |