Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
414 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 91 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. #23762001 | C2 | semidirect |
| 5. #23761755 | C2 | semidirect |
| 6. #23761311 | C2 | semidirect |
| 7. C79×#1299 | C2 | semidirect |
| 192. #1299 | D79 | semidirect |
| 193. C79 | #9352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773223 | 2 |
| #23772418 | 2 |
| #23762001 | 2 |
| #23761835 | 2 |
| #23761755 | 2 |
| #23761311 | 2 |
| C79×#1299 | 2 |
| #9352 | 79 |