Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
714 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 87 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. #23761727 | C2 | semidirect |
| 3. #23761329 | C2 | semidirect |
| 4. #23761327 | C2 | semidirect |
| 5. C79×#1462 | C2 | semidirect |
| 66. C23×D79 | M16 | semidirect |
| 87. C22×Dic79 | M16 | semidirect |
| 254. #1462 | D79 | semidirect |
| 257. C79 | #11502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765975 | 2 |
| #23761727 | 2 |
| #23761329 | 2 |
| #23761327 | 2 |
| C79×#1462 | 2 |
| #11502 | 79 |