Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
496 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23772036 | C2 | semidirect |
| 3. #23761999 | C2 | semidirect |
| 4. #23761997 | C2 | semidirect |
| 5. #23761732 | C2 | semidirect |
| 6. #23761293 | C2 | semidirect |
| 7. C79×#1300 | C2 | semidirect |
| 61. #14579072 | D4 | semidirect |
| 71. #97×C79 | D4 | semidirect |
| 225. #1300 | D79 | semidirect |
| 226. C79 | #9389 | semidirect |
| 287. #97 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772036 | 2 |
| #23769081 | 2 |
| #23761999 | 2 |
| #23761997 | 2 |
| #23761732 | 2 |
| #23761293 | 2 |
| C79×#1300 | 2 |
| #9389 | 79 |