Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
770 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 770 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 |
|---|---|---|
| 3. #23761348 | C2 | direct (N × H) |
| 43. C2×C22⋊C4×C79 | C8 | semidirect |
| 99. C22⋊C4×C79 | C2×C8 | semidirect |
| 197. C2×C79 | #1326 | semidirect |
| 205. C79 | C2×#1326 | semidirect |
| 240. C2×C22⋊C4 | C79⋊C8 | semidirect |
| 300. C22⋊C4 | C2×C79⋊C8 | semidirect |
| 397. C2 | #23761348 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098287 | 2 |
| #23761348 | 2 |
| C2×#385×C79 | 2 |
| C2×#1326 | 79 |