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 |
|---|---|---|
| 85. C2×C4×C157 | Q16 | semidirect |
| 116. C157 | #2056 | semidirect |
| 200. C2×C4 | #14578944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578944 | 2 |
| C2×C4⋊#11929434 | 2 |
| C2×#19097695 | 2 |
| C2×#19097694 | 2 |
| #23757179 | 2 |
| #23757035 | 2 |
| #391×C157 | 2 |
| #2056 | 157 |