Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
416 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 71 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. #23765065 | C2 | semidirect |
| 3. #23761564 | C2 | semidirect |
| 4. #23761562 | C2 | semidirect |
| 5. C79×#2126 | C2 | semidirect |
| 8. #19099113 | C4 | semidirect |
| 11. #19098942 | C4 | semidirect |
| 13. #19098937 | C4 | semidirect |
| 16. C2×C4×C79⋊C8 | C4 | semidirect |
| 176. #2126 | D79 | semidirect |
| 179. C79 | #13583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773826 | 2 |
| #23765065 | 2 |
| #23761564 | 2 |
| #23761562 | 2 |
| C79×#2126 | 2 |
| #13583 | 79 |