Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
154 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 65. Dic157 | Q32 | semidirect |
| 69. C157 | #2209 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic1256 | 2 |
| C2×#19097717 | 2 |
| #23757651 | 2 |
| #23757367 | 2 |
| #23757091 | 2 |
| #23757076 | 2 |
| #358×C157 | 2 |
| #2209 | 157 |