Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
160 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. #23758164 | C2 | semidirect |
| 4. #23758163 | C2 | semidirect |
| 8. #19097846 | C4 | semidirect |
| 11. C2×#14578957 | C4 | semidirect |
| 15. #19097711 | C4 | semidirect |
| 17. C16×D157 | C4 | semidirect |
| 18. M32×C157 | C4 | semidirect |
| 62. C157 | #2110 | semidirect |
| 77. M32 | #10597845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097846 | 2 |
| #23758236 | 2 |
| #23758164 | 2 |
| #23758163 | 2 |
| M32×D157 | 2 |
| #2110 | 157 |