Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
536 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 101 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. C4×#14579167 | C2 | semidirect |
| 3. #23761991 | C2 | semidirect |
| 4. #23761852 | C2 | semidirect |
| 5. #23761840 | C2 | semidirect |
| 6. #23761291 | C2 | semidirect |
| 7. C79×#1278 | C2 | semidirect |
| 219. #1278 | D79 | semidirect |
| 220. C79 | #9211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773461 | 2 |
| C4×#14579167 | 2 |
| #23761991 | 2 |
| #23761852 | 2 |
| #23761840 | 2 |
| #23761291 | 2 |
| C79×#1278 | 2 |
| #9211 | 79 |