Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
384 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#19098385 | C2 | semidirect |
| 4. #23764178 | C2 | semidirect |
| 5. #23761512 | C2 | semidirect |
| 6. #23761485 | C2 | semidirect |
| 18. #19098379 | C4 | semidirect |
| 19. #19098376 | C4 | semidirect |
| 152. C79 | #12952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772317 | 2 |
| C2×#19098385 | 2 |
| #23765149 | 2 |
| #23764178 | 2 |
| #23761512 | 2 |
| #23761485 | 2 |
| C2×#360×C79 | 2 |
| #12952 | 79 |