Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
500 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 4. #23761226 | C2 | semidirect |
| 5. #23761225 | C2 | semidirect |
| 6. #23761225 | C2 | semidirect |
| 7. C79×#1272 | C2 | semidirect |
| 215. #1272 | D79 | semidirect |
| 216. C79 | #7707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771749 | 2 |
| #23763467 | 2 |
| #23763161 | 2 |
| #23761226 | 2 |
| #23761225 | 2 |
| C79×#1272 | 2 |
| #7707 | 79 |