Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
568 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 1. C2×C4×Dic314 | C2 | semidirect |
| 2. #23757211 | C2 | semidirect |
| 3. #23757198 | C2 | semidirect |
| 5. #23757185 | C2 | semidirect |
| 6. C4×C22⋊Dic157 | C2 | semidirect |
| 7. #23757119 | C2 | semidirect |
| 96. C157 | #2398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic314 | 2 |
| #23757211 | 2 |
| #23757198 | 2 |
| #23757187 | 2 |
| #23757185 | 2 |
| C4×C22⋊Dic157 | 2 |
| #23757119 | 2 |
| C2×C4×D4×C157 | 2 |
| #2398 | 157 |