Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
204 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 65 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. C2×#19098401 | C2 | semidirect |
| 2. C22×C79⋊C32 | C2 | semidirect |
| 3. #23765491 | C2 | semidirect |
| 4. #23761601 | C2 | semidirect |
| 5. #23761580 | C2 | semidirect |
| 6. #23761578 | C2 | semidirect |
| 28. C79⋊C32 | D4 | semidirect |
| 82. C22×C79 | SD64 | semidirect |
| 103. C79 | #13696 | semidirect |
| 178. C22 | #19098401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098401 | 2 |
| C22×C79⋊C32 | 2 |
| #23765491 | 2 |
| #23761601 | 2 |
| #23761580 | 2 |
| #23761578 | 2 |
| C79×#2215 | 2 |
| #13696 | 79 |