Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
600 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23763392 | C2 | semidirect |
| 4. #23761517 | C2 | semidirect |
| 5. C79×#1799 | C2 | semidirect |
| 7. C22×(C2×D79)⋊C4 | C4 | semidirect |
| 15. #19098435 | C4 | semidirect |
| 16. #19098418 | C4 | semidirect |
| 17. C4×C22⋊Dic79 | C4 | semidirect |
| 71. C23×D79 | C4⋊C4 | semidirect |
| 88. C22⋊Dic79 | C4⋊C4 | semidirect |
| 242. #1799 | D79 | semidirect |
| 244. C79 | #12795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766054 | 2 |
| C2×#19098349 | 2 |
| #23763392 | 2 |
| #23761517 | 2 |
| C79×#1799 | 2 |
| #12795 | 79 |