Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
218 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 85. C8×C79 | Q32 | semidirect |
| 109. C79 | #12421 | semidirect |
| 187. C8 | #14579107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765552 | 2 |
| #23765450 | 2 |
| #23762997 | 2 |
| #23761464 | 2 |
| #23761459 | 2 |
| #23761448 | 2 |
| C8×Q16×C79 | 2 |
| #12421 | 79 |