Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
610 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 610 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 |
|---|---|---|
| 4. #23763490 | C2 | semidirect |
| 5. #23761972 | C2 | semidirect |
| 6. #23761248 | C2 | semidirect |
| 7. C79×#2502 | C2 | semidirect |
| 127. C22⋊C4×C79 | SD16 | semidirect |
| 213. #2502 | D79 | semidirect |
| 218. C79 | #9951 | semidirect |
| 338. C22⋊C4 | #11929611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774153 | 2 |
| C2×#19098881 | 2 |
| #23764236 | 2 |
| #23763490 | 2 |
| #23761972 | 2 |
| #23761248 | 2 |
| C79×#2502 | 2 |
| #9951 | 79 |