Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
458 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #23763605 | C2 | semidirect |
| 5. #23761288 | C2 | semidirect |
| 6. #23761287 | C2 | semidirect |
| 7. C79×#1855 | C2 | semidirect |
| 160. C2×Dic79 | #108 | semidirect |
| 210. #1855 | D79 | semidirect |
| 214. C79 | #8860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772439 | 2 |
| #23763697 | 2 |
| #23763605 | 2 |
| #23761716 | 2 |
| #23761288 | 2 |
| #23761287 | 2 |
| C79×#1855 | 2 |
| #8860 | 79 |