Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
798 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 227 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. #23773959 | C2 | semidirect |
| 2. #23773914 | C2 | semidirect |
| 4. #23763033 | C2 | semidirect |
| 5. #23763028 | C2 | semidirect |
| 6. #23763022 | C2 | semidirect |
| 7. C2×#322×C79 | C2 | semidirect |
| 79. C2×C8×C79 | SD16 | semidirect |
| 127. C2×#322 | D79 | semidirect |
| 128. C79 | #19608 | semidirect |
| 193. C2×C8 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773959 | 2 |
| #23773914 | 2 |
| #23773828 | 2 |
| #23763033 | 2 |
| #23763028 | 2 |
| #23763022 | 2 |
| C2×#322×C79 | 2 |
| #19608 | 79 |