Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
268 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 1. #23765629 | C2 | semidirect |
| 4. #23761317 | C2 | semidirect |
| 5. C79×#1713 | C2 | semidirect |
| 79. #1713 | D79 | semidirect |
| 82. C79 | #12512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765629 | 2 |
| #23765625 | 2 |
| #23763006 | 2 |
| #23761317 | 2 |
| C79×#1713 | 2 |
| #12512 | 79 |