Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
380 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 380 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. #23763553 | C2 | semidirect |
| 3. #23762185 | C2 | semidirect |
| 6. #23761294 | C2 | semidirect |
| 7. C79×#1283 | C2 | semidirect |
| 186. #1283 | D79 | semidirect |
| 187. C79 | #8876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772536 | 2 |
| #23763553 | 2 |
| #23762185 | 2 |
| #23761887 | 2 |
| #23761814 | 2 |
| #23761294 | 2 |
| C79×#1283 | 2 |
| #8876 | 79 |