Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
390 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23774741 | C2 | semidirect |
| 4. #23761413 | C2 | semidirect |
| 5. #23761412 | C2 | semidirect |
| 6. #23761339 | C2 | semidirect |
| 140. C2×Dic79 | SD32 | semidirect |
| 183. C79 | #12159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774741 | 2 |
| #23765329 | 2 |
| #23764708 | 2 |
| #23761413 | 2 |
| #23761412 | 2 |
| #23761339 | 2 |
| C79×#2187 | 2 |
| #12159 | 79 |