Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
456 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23762003 | C2 | semidirect |
| 5. #23761757 | C2 | semidirect |
| 6. #23761250 | C2 | semidirect |
| 7. C79×#1290 | C2 | semidirect |
| 209. #1290 | D79 | semidirect |
| 211. C79 | #9245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098864 | 2 |
| #23772437 | 2 |
| #23762003 | 2 |
| #23761842 | 2 |
| #23761757 | 2 |
| #23761250 | 2 |
| C79×#1290 | 2 |
| #9245 | 79 |