Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
132 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 8. C2×#14578957 | C4 | semidirect |
| 12. #19097711 | C4 | semidirect |
| 15. M32×C157 | C4 | semidirect |
| 58. C157 | #1378 | semidirect |
| 70. 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 |
| M32×D157 | 2 |
| #1378 | 157 |