Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
332 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23761574 | C2 | semidirect |
| 4. #23761559 | C2 | semidirect |
| 6. #19099175 | C4 | semidirect |
| 8. #19098935 | C4 | semidirect |
| 9. #19098927 | C4 | semidirect |
| 15. #19098624 | C4 | semidirect |
| 28. #14579161 | C2×C4 | semidirect |
| 30. #14579153 | C2×C4 | semidirect |
| 42. #14579072 | C2×C4 | semidirect |
| 43. C4×C79⋊C8 | C2×C4 | semidirect |
| 158. C79 | #13607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774472 | 2 |
| #23765092 | 2 |
| #23761574 | 2 |
| #23761559 | 2 |
| C79×#2127 | 2 |
| #13607 | 79 |