Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
428 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23765189 | C2 | semidirect |
| 2. C2×#19098376 | C2 | semidirect |
| 3. C2×#19098364 | C2 | semidirect |
| 4. C2×#19098347 | C2 | semidirect |
| 5. #23763464 | C2 | semidirect |
| 6. #23761495 | C2 | semidirect |
| 30. #14579101 | D4 | semidirect |
| 191. C79 | #13387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765189 | 2 |
| C2×#19098376 | 2 |
| C2×#19098364 | 2 |
| C2×#19098347 | 2 |
| #23763464 | 2 |
| #23761495 | 2 |
| C79×#3058 | 2 |
| #13387 | 79 |