Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
312 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23765202 | C2 | semidirect |
| 3. #334×D79 | C2 | semidirect |
| 4. #23761453 | C2 | semidirect |
| 5. #23761451 | C2 | semidirect |
| 6. #23761443 | C2 | semidirect |
| 7. C79×#1360 | C2 | semidirect |
| 156. #1360 | D79 | semidirect |
| 157. C79 | #11945 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773967 | 2 |
| #23765202 | 2 |
| #334×D79 | 2 |
| #23761453 | 2 |
| #23761451 | 2 |
| #23761443 | 2 |
| C79×#1360 | 2 |
| #11945 | 79 |