Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
412 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23764388 | C2 | semidirect |
| 4. #23762125 | C2 | semidirect |
| 6. #23761273 | C2 | semidirect |
| 7. C79×#1307 | C2 | semidirect |
| 187. #1307 | D79 | semidirect |
| 189. C79 | #9337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774429 | 2 |
| #23772567 | 2 |
| #23764388 | 2 |
| #23762125 | 2 |
| #23762008 | 2 |
| #23761273 | 2 |
| C79×#1307 | 2 |
| #9337 | 79 |