Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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×#19097705 | C2 | semidirect |
| 3. C2×#19097693 | C2 | semidirect |
| 4. #23757175 | C2 | semidirect |
| 5. C2×C4×C8×C157 | C2 | semidirect |
| 9. C2×D1256 | C4 | semidirect |
| 54. C2×C4×C157 | D8 | semidirect |
| 62. C8×C157 | C22⋊C4 | semidirect |
| 85. C157 | #1970 | semidirect |
| 90. C2×C4×C8 | D157 | semidirect |
| 140. C2×C4 | D1256 | semidirect |
| 148. C8 | #14578931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1256 | 2 |
| C2×#19097705 | 2 |
| C2×#19097693 | 2 |
| #23757175 | 2 |
| C2×C4×C8×C157 | 2 |
| #1970 | 157 |