Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
316 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 34. #14579101 | Q8 | semidirect |
| 50. M32×C79 | Q8 | semidirect |
| 133. C79 | #13270 | semidirect |
| 167. M32 | Dic158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772332 | 2 |
| #23765165 | 2 |
| #23765004 | 2 |
| #23761486 | 2 |
| #23761481 | 2 |
| C79×#1378 | 2 |
| #13270 | 79 |