Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
212 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 118 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. #23758114 | C2 | semidirect |
| 3. C8×#11929441 | C2 | semidirect |
| 17. C2×#11929434 | C8 | semidirect |
| 24. C2×C8×C157 | C8 | semidirect |
| 51. C157 | #1450 | semidirect |
| 73. C2×C8 | #11929441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758289 | 2 |
| #23758114 | 2 |
| C8×#11929441 | 2 |
| C2×C8×Dic157 | 2 |
| #1450 | 157 |