Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
542 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 95 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×#19098972 | C2 | semidirect |
| 4. #23764220 | C2 | semidirect |
| 5. C2×#19098304 | C2 | semidirect |
| 6. #23761282 | C2 | semidirect |
| 199. C79 | #10086 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098972 | 2 |
| C2×#19098922 | 2 |
| #23771451 | 2 |
| #23764220 | 2 |
| C2×#19098304 | 2 |
| #23761282 | 2 |
| C2×#329×C79 | 2 |
| #10086 | 79 |