Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
434 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23764322 | C2 | semidirect |
| 4. #23762116 | C2 | semidirect |
| 6. #23761255 | C2 | semidirect |
| 7. C79×#1290 | C2 | semidirect |
| 10. #19098972 | C4 | semidirect |
| 11. #19098923 | C4 | semidirect |
| 200. #1290 | D79 | semidirect |
| 202. C79 | #9377 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774632 | 2 |
| #23772536 | 2 |
| #23764322 | 2 |
| #23762116 | 2 |
| #23761926 | 2 |
| #23761255 | 2 |
| C79×#1290 | 2 |
| #9377 | 79 |