Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
536 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 1. #23771359 | C2 | semidirect |
| 5. #23761225 | C2 | semidirect |
| 6. #23761222 | C2 | semidirect |
| 7. C79×#1272 | C2 | semidirect |
| 69. C2×Dic158 | SD16 | semidirect |
| 100. C4⋊Dic79 | SD16 | semidirect |
| 222. #1272 | D79 | semidirect |
| 224. C79 | #7748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771359 | 2 |
| #23764635 | 2 |
| #23764490 | 2 |
| #23764487 | 2 |
| #23761225 | 2 |
| #23761222 | 2 |
| C79×#1272 | 2 |
| #7748 | 79 |