Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
424 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19097771 | C2 | semidirect |
| 3. #23757633 | C2 | semidirect |
| 4. #23757624 | C2 | semidirect |
| 5. #23757620 | C2 | semidirect |
| 6. #23757275 | C2 | semidirect |
| 7. C4×M16×C157 | C2 | semidirect |
| 100. C157 | #3141 | semidirect |
| 108. C4×M16 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757823 | 2 |
| C2×#19097771 | 2 |
| #23757633 | 2 |
| #23757624 | 2 |
| #23757620 | 2 |
| #23757275 | 2 |
| C4×M16×C157 | 2 |
| #3141 | 157 |