Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
3998 conjugacy classes of subgroups; only the 467 normal subgroups are shown.
This group has 3998 conjugacy classes of subgroups — too many to draw. Only its 467 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 |
|---|---|---|
| 3. #23761671 | C2 | semidirect |
| 4. #23761670 | C2 | semidirect |
| 5. C79×#1446 | C2 | semidirect |
| 8. C22×Q8×D79 | C4 | semidirect |
| 111. #1446 | D79 | semidirect |
| 112. C79 | #14336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Q8×D79 | 2 |
| C2×#19098425 | 2 |
| #23761671 | 2 |
| #23761670 | 2 |
| C79×#1446 | 2 |
| #14336 | 79 |