Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
360 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 2. #23762183 | C2 | semidirect |
| 5. #23761293 | C2 | semidirect |
| 6. #23761250 | C2 | semidirect |
| 7. C79×#1832 | C2 | semidirect |
| 178. #1832 | D79 | semidirect |
| 184. C79 | #8877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772536 | 2 |
| #23762183 | 2 |
| #23761884 | 2 |
| #23761811 | 2 |
| #23761293 | 2 |
| #23761250 | 2 |
| C79×#1832 | 2 |
| #8877 | 79 |