Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
218 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 218 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 |
|---|---|---|
| 1. #23765673 | C2 | semidirect |
| 4. #23761473 | C2 | semidirect |
| 5. #23761456 | C2 | semidirect |
| 6. #23761455 | C2 | semidirect |
| 51. C79⋊C16 | SD16 | semidirect |
| 112. C79 | #12454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765673 | 2 |
| #23765232 | 2 |
| #23762789 | 2 |
| #23761473 | 2 |
| #23761456 | 2 |
| #23761455 | 2 |
| C79×#1673 | 2 |
| #12454 | 79 |