Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 9. #19098591 | C4 | semidirect |
| 10. #19098589 | C4 | semidirect |
| 13. M16×Dic79 | C4 | semidirect |
| 14. C2×C8×Dic79 | C4 | semidirect |
| 123. C79 | #12864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772040 | 2 |
| #23763505 | 2 |
| #23761530 | 2 |
| #23761521 | 2 |
| C79×#1392 | 2 |
| #12864 | 79 |