Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
384 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#19098386 | C2 | semidirect |
| 5. #23764180 | C2 | semidirect |
| 6. #23761512 | C2 | semidirect |
| 7. C79×#1378 | C2 | semidirect |
| 18. #19098380 | C4 | semidirect |
| 19. #19098377 | C4 | semidirect |
| 151. #1378 | D79 | semidirect |
| 152. C79 | #12952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772318 | 2 |
| C2×#19098386 | 2 |
| #23765150 | 2 |
| C2×#19098374 | 2 |
| #23764180 | 2 |
| #23761512 | 2 |
| C79×#1378 | 2 |
| #12952 | 79 |