Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 56. Q16×C79 | Q16 | semidirect |
| 105. C79 | #12448 | semidirect |
| 147. Q16 | #11929614 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765552 | 2 |
| #23763017 | 2 |
| Q16×C79⋊C8 | 2 |
| #23761469 | 2 |
| #23761458 | 2 |
| #23761457 | 2 |
| C79×#2227 | 2 |
| #12448 | 79 |