Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
686 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #23761714 | C2 | semidirect |
| 3. #23761327 | C2 | semidirect |
| 4. C79×#1458 | C2 | semidirect |
| 27. C22×D316 | C8 | semidirect |
| 187. #1458 | D79 | semidirect |
| 189. C79 | #11427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765980 | 2 |
| #23761714 | 2 |
| #23761327 | 2 |
| C79×#1458 | 2 |
| #11427 | 79 |