Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
338 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23765583 | C2 | semidirect |
| 3. #23765581 | C2 | semidirect |
| 4. #23764842 | C2 | semidirect |
| 5. #23761414 | C2 | semidirect |
| 6. #23761325 | C2 | semidirect |
| 7. C79×#1349 | C2 | semidirect |
| 15. C2×#14579095 | C22 | semidirect |
| 22. C22⋊(C79⋊C16) | C22 | semidirect |
| 25. C22⋊C16×C79 | C22 | semidirect |
| 26. #341×C79 | C22 | semidirect |
| 169. #1349 | D79 | semidirect |
| 171. C79 | #12284 | semidirect |
| 188. C22⋊C16 | C2×D79 | semidirect |
| 190. #341 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774260 | 2 |
| #23765583 | 2 |
| #23765581 | 2 |
| #23764842 | 2 |
| #23761414 | 2 |
| #23761325 | 2 |
| C79×#1349 | 2 |
| #12284 | 79 |