Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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. #23762170 | C2 | semidirect |
| 4. #23761964 | C2 | semidirect |
| 6. #23761259 | C2 | semidirect |
| 7. C79×#1542 | C2 | semidirect |
| 176. #1542 | D79 | semidirect |
| 180. C79 | #10468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773193 | 2 |
| #23763411 | 2 |
| #23762170 | 2 |
| #23761964 | 2 |
| #23761720 | 2 |
| #23761259 | 2 |
| C79×#1542 | 2 |
| #10468 | 79 |