Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23765194 | C2 | semidirect |
| 5. #23764191 | C2 | semidirect |
| 6. #23761488 | C2 | semidirect |
| 7. C79×#1381 | C2 | semidirect |
| 18. #19098378 | C4 | semidirect |
| 19. #19098375 | C4 | semidirect |
| 147. #1381 | D79 | semidirect |
| 149. C79 | #12942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772316 | 2 |
| #23765194 | 2 |
| #23765147 | 2 |
| C2×#19098371 | 2 |
| #23764191 | 2 |
| #23761488 | 2 |
| C79×#1381 | 2 |
| #12942 | 79 |