Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
258 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. #23762170 | C2 | semidirect |
| 5. #23761310 | C2 | semidirect |
| 6. #23761263 | C2 | semidirect |
| 7. C79×#1290 | C2 | semidirect |
| 126. #1290 | D79 | semidirect |
| 128. C79 | #10647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23762170 | 2 |
| #23762123 | 2 |
| #23762093 | 2 |
| #23761868 | 2 |
| #23761310 | 2 |
| #23761263 | 2 |
| C79×#1290 | 2 |
| #10647 | 79 |