Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
320 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23765197 | C2 | semidirect |
| 3. #335×D79 | C2 | semidirect |
| 4. #23761365 | C2 | semidirect |
| 5. #23761363 | C2 | semidirect |
| 6. #23761361 | C2 | semidirect |
| 7. C79×#1331 | C2 | semidirect |
| 160. #1331 | D79 | semidirect |
| 161. C79 | #11648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773968 | 2 |
| #23765197 | 2 |
| #335×D79 | 2 |
| #23761365 | 2 |
| #23761363 | 2 |
| #23761361 | 2 |
| C79×#1331 | 2 |
| #11648 | 79 |