Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
330 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 87 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. #23765657 | C2 | semidirect |
| 2. #23765655 | C2 | semidirect |
| 3. #23765652 | C2 | semidirect |
| 5. #23763006 | C2 | semidirect |
| 6. C8×C79⋊C16 | C2 | semidirect |
| 7. C79×#1709 | C2 | semidirect |
| 104. #1709 | D79 | semidirect |
| 106. C79 | #12518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765657 | 2 |
| #23765655 | 2 |
| #23765652 | 2 |
| #23765649 | 2 |
| #23763006 | 2 |
| C8×C79⋊C16 | 2 |
| C79×#1709 | 2 |
| #12518 | 79 |