Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
740 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 740 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. #23774341 | C2 | semidirect |
| 2. #23773197 | C2 | semidirect |
| 3. #23762068 | C2 | semidirect |
| 4. #23761898 | C2 | semidirect |
| 5. #23761791 | C2 | semidirect |
| 6. #23761303 | C2 | semidirect |
| 33. #14579161 | D4 | semidirect |
| 34. #14579161 | D4 | semidirect |
| 45. C4⋊(C79⋊C8) | D4 | semidirect |
| 46. C4⋊(C79⋊C8) | D4 | semidirect |
| 116. C2×D4×C79 | SD16 | semidirect |
| 229. C79 | #10246 | semidirect |
| 324. C2×D4 | #11929612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774341 | 2 |
| #23773197 | 2 |
| #23762068 | 2 |
| #23761898 | 2 |
| #23761791 | 2 |
| #23761303 | 2 |
| C79×#2541 | 2 |
| #10246 | 79 |