Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
580 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23774717 | C2 | semidirect |
| 2. #23773197 | C2 | semidirect |
| 4. #23761856 | C2 | semidirect |
| 5. #23761852 | C2 | semidirect |
| 6. #23761275 | C2 | semidirect |
| 7. C79×#1954 | C2 | semidirect |
| 124. C2×D4×C79 | SD16 | semidirect |
| 233. #1954 | D79 | semidirect |
| 237. C79 | #10256 | semidirect |
| 332. C2×D4 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774717 | 2 |
| #23773197 | 2 |
| #23772864 | 2 |
| #23761856 | 2 |
| #23761852 | 2 |
| #23761275 | 2 |
| C79×#1954 | 2 |
| #10256 | 79 |