Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
398 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 73 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. #23769043 | C2 | semidirect |
| 5. #23761292 | C2 | semidirect |
| 6. #23761266 | C2 | semidirect |
| 7. C79×#1285 | C2 | semidirect |
| 30. #14579161 | Q8 | semidirect |
| 31. #14579158 | Q8 | semidirect |
| 188. #1285 | D79 | semidirect |
| 189. C79 | #10378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769043 | 2 |
| #23764318 | 2 |
| #23761948 | 2 |
| #23761909 | 2 |
| #23761292 | 2 |
| #23761266 | 2 |
| C79×#1285 | 2 |
| #10378 | 79 |