Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
316 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23765195 | C2 | semidirect |
| 2. #23765165 | C2 | semidirect |
| 5. #23764188 | C2 | semidirect |
| 6. #23761503 | C2 | semidirect |
| 138. C79 | #13472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765195 | 2 |
| #23765165 | 2 |
| C2×#19098376 | 2 |
| #23764311 | 2 |
| #23764188 | 2 |
| #23761503 | 2 |
| C2×#361×C79 | 2 |
| #13472 | 79 |