Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
306 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 306 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 |
|---|---|---|
| 4. #23761383 | C2 | semidirect |
| 5. #23761382 | C2 | semidirect |
| 6. #23761381 | C2 | semidirect |
| 7. C79×#1338 | C2 | semidirect |
| 151. #1338 | D79 | semidirect |
| 152. C79 | #11644 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #446×D79 | 2 |
| #23765202 | 2 |
| #23765201 | 2 |
| #23761383 | 2 |
| #23761382 | 2 |
| #23761381 | 2 |
| C79×#1338 | 2 |
| #11644 | 79 |