Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
372 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 2. #23765639 | C2 | semidirect |
| 3. #23765544 | C2 | semidirect |
| 4. #23761442 | C2 | semidirect |
| 5. #23761366 | C2 | semidirect |
| 6. #23761358 | C2 | semidirect |
| 7. C79×#1693 | C2 | semidirect |
| 17. C4⋊(C79⋊C16) | C22 | semidirect |
| 21. #19098339 | C22 | semidirect |
| 22. #500×C79 | C22 | semidirect |
| 25. #334×C79 | C22 | semidirect |
| 82. D632 | SD16 | semidirect |
| 170. #1693 | D79 | semidirect |
| 174. C79 | #12378 | semidirect |
| 177. #500 | C2×D79 | semidirect |
| 192. #334 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775012 | 2 |
| #23765639 | 2 |
| #23765544 | 2 |
| #23761442 | 2 |
| #23761366 | 2 |
| #23761358 | 2 |
| C79×#1693 | 2 |
| #12378 | 79 |