Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
318 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 318 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. #23765600 | C2 | semidirect |
| 3. #23765581 | C2 | semidirect |
| 4. #23764842 | C2 | semidirect |
| 5. #23761414 | C2 | semidirect |
| 6. #23761325 | C2 | semidirect |
| 7. C79×#1350 | C2 | semidirect |
| 161. #1350 | D79 | semidirect |
| 164. C79 | #12287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774303 | 2 |
| #23765600 | 2 |
| #23765581 | 2 |
| #23764842 | 2 |
| #23761414 | 2 |
| #23761325 | 2 |
| C79×#1350 | 2 |
| #12287 | 79 |