Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
744 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 108. C22⋊Dic79 | Q16 | semidirect |
| 227. C79 | #9957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774175 | 2 |
| C2×#19098719 | 2 |
| #23767040 | 2 |
| #23764384 | 2 |
| #23761971 | 2 |
| #23761247 | 2 |
| C79×#1787 | 2 |
| #9957 | 79 |