Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
526 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23774742 | C2 | semidirect |
| 4. #23761855 | C2 | semidirect |
| 5. #23761854 | C2 | semidirect |
| 6. #23761274 | C2 | semidirect |
| 110. C2×D4×C79 | Q16 | semidirect |
| 218. C79 | #10258 | semidirect |
| 304. C2×D4 | #11929614 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774742 | 2 |
| #23773197 | 2 |
| #23764195 | 2 |
| #23761855 | 2 |
| #23761854 | 2 |
| #23761274 | 2 |
| C79×#3077 | 2 |
| #10258 | 79 |