Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23763007 | C2 | semidirect |
| 3. D8×C79⋊C8 | C2 | semidirect |
| 4. #23761469 | C2 | semidirect |
| 5. #23761449 | C2 | semidirect |
| 6. #23761447 | C2 | semidirect |
| 7. C79×#2208 | C2 | semidirect |
| 119. #2208 | D79 | semidirect |
| 126. C79 | #12428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765435 | 2 |
| #23763007 | 2 |
| D8×C79⋊C8 | 2 |
| #23761469 | 2 |
| #23761449 | 2 |
| #23761447 | 2 |
| C79×#2208 | 2 |
| #12428 | 79 |