Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1072 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 175 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. #23773949 | C2 | semidirect |
| 3. #23773218 | C2 | semidirect |
| 4. #23764610 | C2 | semidirect |
| 5. #23764381 | C2 | semidirect |
| 6. #23764241 | C2 | semidirect |
| 7. #23763609 | C2 | semidirect |
| 8. #23763211 | C2 | semidirect |
| 9. C79×#2641 | C2 | semidirect |
| 102. #11929608 | #41 | semidirect |
| 203. #2641 | D79 | semidirect |
| 209. C79 | #25690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777274 | 2 |
| #23773949 | 2 |
| #23773218 | 2 |
| #23764610 | 2 |
| #23764381 | 2 |
| #23764241 | 2 |
| #23763609 | 2 |
| #23763211 | 2 |
| C79×#2641 | 2 |
| #25690 | 79 |