Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
608 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 608 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. #23763681 | C2 | semidirect |
| 4. #23763610 | C2 | semidirect |
| 5. #23761524 | C2 | semidirect |
| 6. #23761517 | C2 | semidirect |
| 20. #19098350 | C4 | semidirect |
| 104. C24×C79 | C4⋊C4 | semidirect |
| 136. C22⋊C4×C79 | C4⋊C4 | semidirect |
| 266. C79 | #12960 | semidirect |
| 338. C24 | Dic79⋊C4 | semidirect |
| 393. C22⋊C4 | Dic79⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766541 | 2 |
| C2×#19098350 | 2 |
| #23763681 | 2 |
| #23763610 | 2 |
| #23761524 | 2 |
| #23761517 | 2 |
| C79×#1889 | 2 |
| #12960 | 79 |