Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
306 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 89. Q8×C79 | Q32 | semidirect |
| 133. C79 | #12334 | semidirect |
| 221. Q8 | Dic632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776406 | 2 |
| #23765653 | 2 |
| #23765451 | 2 |
| #23762770 | 2 |
| #23761450 | 2 |
| #23761365 | 2 |
| C79×Q8⋊C16 | 2 |
| #12334 | 79 |