Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
562 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 562 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. C2×#19098881 | C2 | semidirect |
| 3. C2×#19098876 | C2 | semidirect |
| 4. #23761761 | C2 | semidirect |
| 5. #23761761 | C2 | semidirect |
| 6. #23761287 | C2 | semidirect |
| 7. C79×#1821 | C2 | semidirect |
| 206. #1821 | D79 | semidirect |
| 210. C79 | #9992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774200 | 2 |
| C2×#19098881 | 2 |
| C2×#19098876 | 2 |
| #23761761 | 2 |
| #23761287 | 2 |
| C79×#1821 | 2 |
| #9992 | 79 |