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 |
|---|---|---|
| 44. C2×Dic157 | Q16 | semidirect |
| 76. C157 | #2056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097700 | 2 |
| C2×#19097695 | 2 |
| #23757180 | 2 |
| #23757036 | 2 |
| C22×Q16×C157 | 2 |
| #2056 | 157 |