Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
322 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23765620 | C2 | semidirect |
| 3. #23765612 | C2 | semidirect |
| 4. #23764954 | C2 | semidirect |
| 5. #23761387 | C2 | semidirect |
| 6. #23761337 | C2 | semidirect |
| 7. C79×#1339 | C2 | semidirect |
| 159. #1339 | D79 | semidirect |
| 161. C79 | #12303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774311 | 2 |
| #23765620 | 2 |
| #23765612 | 2 |
| #23764954 | 2 |
| #23761387 | 2 |
| #23761337 | 2 |
| C79×#1339 | 2 |
| #12303 | 79 |