Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
794 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 139 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. C2×#19098755 | C2 | semidirect |
| 2. #23764194 | C2 | semidirect |
| 3. C2×#19098307 | C2 | semidirect |
| 4. #23761235 | C2 | semidirect |
| 5. C2×#493×C79 | C2 | semidirect |
| 52. C2×D316 | D8 | semidirect |
| 86. C2×C8×C79 | D8 | semidirect |
| 159. C2×#493 | D79 | semidirect |
| 164. C79 | #10260 | semidirect |
| 243. C2×C8 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098755 | 2 |
| #23764194 | 2 |
| C2×#19098307 | 2 |
| #23761235 | 2 |
| C2×#493×C79 | 2 |
| #10260 | 79 |