Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
406 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 406 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. #23765476 | C2 | semidirect |
| 2. #23763014 | C2 | semidirect |
| 3. #23761437 | C2 | semidirect |
| 4. #23761373 | C2 | semidirect |
| 5. C79×#3292 | C2 | semidirect |
| 7. #19098940 | C22 | semidirect |
| 9. #19098384 | C22 | semidirect |
| 11. C8×C79⋊C8 | C22 | semidirect |
| 50. Q16×C79 | D8 | semidirect |
| 56. D8×C79 | D8 | semidirect |
| 97. #3292 | D79 | semidirect |
| 102. C79 | #12310 | semidirect |
| 142. Q16 | #11929609 | semidirect |
| 151. D8 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765476 | 2 |
| #23763014 | 2 |
| #23761437 | 2 |
| #23761373 | 2 |
| C79×#3292 | 2 |
| #12310 | 79 |