Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
398 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23771233 | C2 | semidirect |
| 2. #23764621 | C2 | semidirect |
| 3. #23762437 | C2 | semidirect |
| 4. #23761428 | C2 | semidirect |
| 5. #23761403 | C2 | semidirect |
| 6. #23761345 | C2 | semidirect |
| 198. C79 | #12144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771233 | 2 |
| #23764621 | 2 |
| #23762437 | 2 |
| #23761428 | 2 |
| #23761403 | 2 |
| #23761345 | 2 |
| C79×#1598 | 2 |
| #12144 | 79 |