Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
534 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 534 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 |
|---|---|---|
| 3. #23764385 | C2 | semidirect |
| 4. #23761934 | C2 | semidirect |
| 5. #23761305 | C2 | semidirect |
| 6. #23761253 | C2 | semidirect |
| 10. #19098874 | C4 | semidirect |
| 13. #19098701 | C4 | semidirect |
| 31. C22×Dic158 | C2×C4 | semidirect |
| 41. C2×C4⋊Dic79 | C2×C4 | semidirect |
| 55. C22⋊(C79⋊C8) | C2×C4 | semidirect |
| 237. C79 | #9341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774206 | 2 |
| #23766557 | 2 |
| #23764385 | 2 |
| #23761934 | 2 |
| #23761305 | 2 |
| #23761253 | 2 |
| C79×#1507 | 2 |
| #9341 | 79 |