Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
288 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23757011 | C2 | semidirect |
| 5. C22×Dic314 | C4 | semidirect |
| 8. #19097750 | C4 | semidirect |
| 11. C2×C4⋊Dic157 | C4 | semidirect |
| 98. C157 | #1520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097750 | 2 |
| #23757133 | 2 |
| #23757011 | 2 |
| C2×C22⋊C8×C157 | 2 |
| #1520 | 157 |