Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
298 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. C2×C32×D79 | C2 | semidirect |
| 3. #23765181 | C2 | semidirect |
| 4. #23761582 | C2 | semidirect |
| 5. #23761580 | C2 | semidirect |
| 6. #23761578 | C2 | semidirect |
| 7. C79×#1415 | C2 | semidirect |
| 10. #19098992 | C4 | semidirect |
| 110. #1415 | D79 | semidirect |
| 111. C79 | #13615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098992 | 2 |
| C2×C32×D79 | 2 |
| #23765181 | 2 |
| #23761582 | 2 |
| #23761580 | 2 |
| #23761578 | 2 |
| C79×#1415 | 2 |
| #13615 | 79 |