Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
346 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 67. C2×Dic158 | Q16 | semidirect |
| 168. C79 | #12222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771288 | 2 |
| #23764558 | 2 |
| #23762374 | 2 |
| #23761431 | 2 |
| #23761427 | 2 |
| #23761333 | 2 |
| C79×#1617 | 2 |
| #12222 | 79 |