Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
316 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 316 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. #23765093 | C2 | semidirect |
| 3. #23765088 | C2 | semidirect |
| 4. #23761573 | C2 | semidirect |
| 5. #23761566 | C2 | semidirect |
| 6. #23761566 | C2 | semidirect |
| 7. C79×#1413 | C2 | semidirect |
| 162. #1413 | D79 | semidirect |
| 165. C79 | #13611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774462 | 2 |
| #23765093 | 2 |
| #23765088 | 2 |
| #23761573 | 2 |
| #23761566 | 2 |
| C79×#1413 | 2 |
| #13611 | 79 |