Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 426 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. #23762015 | C2 | semidirect |
| 5. #23761263 | C2 | semidirect |
| 6. #23761230 | C2 | semidirect |
| 7. C79×#1497 | C2 | semidirect |
| 172. #1497 | D79 | semidirect |
| 175. C79 | #9285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774352 | 2 |
| #23772475 | 2 |
| #23762015 | 2 |
| #23762012 | 2 |
| #23761263 | 2 |
| #23761230 | 2 |
| C79×#1497 | 2 |
| #9285 | 79 |