Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
288 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 3. #23762801 | C2 | semidirect |
| 4. #23761449 | C2 | semidirect |
| 5. #23761380 | C2 | semidirect |
| 7. C79×#2241 | C2 | semidirect |
| 126. #2241 | D79 | semidirect |
| 132. C79 | #12387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776390 | 2 |
| #23765544 | 2 |
| #23762801 | 2 |
| #23761449 | 2 |
| #23761380 | 2 |
| #23761362 | 2 |
| C79×#2241 | 2 |
| #12387 | 79 |