Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
346 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23775747 | C2 | semidirect |
| 2. #23765625 | C2 | semidirect |
| 3. #23765436 | C2 | semidirect |
| 4. #23762756 | C2 | semidirect |
| 5. #23761360 | C2 | semidirect |
| 6. #23761354 | C2 | semidirect |
| 7. C79×#1364 | C2 | semidirect |
| 108. D316 | D16 | semidirect |
| 148. #1364 | D79 | semidirect |
| 151. C79 | #12340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775747 | 2 |
| #23765625 | 2 |
| #23765436 | 2 |
| #23762756 | 2 |
| #23761360 | 2 |
| #23761354 | 2 |
| C79×#1364 | 2 |
| #12340 | 79 |