Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
588 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 1. #23771393 | C2 | semidirect |
| 3. #23761226 | C2 | semidirect |
| 4. #23761225 | C2 | semidirect |
| 51. C2×Dic158 | SD16 | semidirect |
| 66. C2×Q8×C79 | SD16 | semidirect |
| 159. C79 | #7749 | semidirect |
| 210. C2×Q8 | #11929612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771393 | 2 |
| #23764488 | 2 |
| #23761226 | 2 |
| #23761225 | 2 |
| C79×#2014 | 2 |
| #7749 | 79 |