Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
356 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 99 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×#19098387 | C2 | semidirect |
| 4. #23763287 | C2 | semidirect |
| 5. #23761506 | C2 | semidirect |
| 6. #23761479 | C2 | semidirect |
| 16. #19098364 | C4 | semidirect |
| 145. C79 | #13142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098387 | 2 |
| #23765116 | 2 |
| #23764277 | 2 |
| #23763287 | 2 |
| #23761506 | 2 |
| #23761479 | 2 |
| C2×#361×C79 | 2 |
| #13142 | 79 |