Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
294 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 59 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. #23776536 | C2 | semidirect |
| 2. #23765713 | C2 | semidirect |
| 3. #23761586 | C2 | semidirect |
| 4. #23761540 | C2 | semidirect |
| 5. C79×#2218 | C2 | semidirect |
| 13. #19098397 | C22 | semidirect |
| 14. C2×D16×C79 | C22 | semidirect |
| 17. #367×C79 | C22 | semidirect |
| 28. Dic632 | D4 | semidirect |
| 32. D1264 | D4 | semidirect |
| 114. #2218 | D79 | semidirect |
| 117. C79 | #13667 | semidirect |
| 123. C2×D16 | C2×D79 | semidirect |
| 129. #367 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776536 | 2 |
| #23765713 | 2 |
| #23761586 | 2 |
| #23761540 | 2 |
| C79×#2218 | 2 |
| #13667 | 79 |