Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
412 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23765165 | C2 | semidirect |
| 5. #23763525 | C2 | semidirect |
| 6. #23761501 | C2 | semidirect |
| 7. C79×#1389 | C2 | semidirect |
| 11. #19098674 | C4 | semidirect |
| 143. #1389 | D79 | semidirect |
| 145. C79 | #12826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772251 | 2 |
| #23765165 | 2 |
| C2×#19098375 | 2 |
| #23765117 | 2 |
| #23763525 | 2 |
| #23761501 | 2 |
| C79×#1389 | 2 |
| #12826 | 79 |