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 |
| 5. #23761411 | C2 | semidirect |
| 6. #23761339 | C2 | semidirect |
| 7. C79×#1348 | C2 | semidirect |
| 136. C2×Dic79 | SD32 | semidirect |
| 181. #1348 | D79 | 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 |
| #23765331 | 2 |
| #23765328 | 2 |
| #23764712 | 2 |
| #23761411 | 2 |
| #23761339 | 2 |
| C79×#1348 | 2 |
| #12159 | 79 |