Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
316 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19097705 | C2 | semidirect |
| 2. C2×#19097703 | C2 | semidirect |
| 4. #23757036 | C2 | semidirect |
| 15. C2×M16×C157 | C4 | semidirect |
| 67. C8×C157 | C22⋊C4 | semidirect |
| 91. C157 | #1809 | semidirect |
| 101. C2×M16 | Dic157 | semidirect |
| 159. C8 | C22⋊Dic157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097705 | 2 |
| C2×#19097703 | 2 |
| #23757133 | 2 |
| #23757036 | 2 |
| C22×M16×C157 | 2 |
| #1809 | 157 |