Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
618 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 2. #23761334 | C2 | direct (N × H) |
| 22. C22×Q8×C79 | C8 | semidirect |
| 51. C2×Q8×C79 | C2×C8 | semidirect |
| 139. C2×C79 | #1319 | semidirect |
| 146. C79 | C2×#1319 | semidirect |
| 162. C22×Q8 | C79⋊C8 | semidirect |
| 192. C2×Q8 | C2×C79⋊C8 | semidirect |
| 281. C2 | #23761334 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098289 | 2 |
| #23761334 | 2 |
| C2×#391×C79 | 2 |
| C2×#1319 | 79 |