Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
168 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23761601 | C2 | semidirect |
| 4. #23761600 | C2 | semidirect |
| 5. #23761581 | C2 | semidirect |
| 7. C79×#1416 | C2 | semidirect |
| 89. #1416 | D79 | semidirect |
| 91. C79 | #13716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765488 | 2 |
| #23765181 | 2 |
| #23761601 | 2 |
| #23761600 | 2 |
| #23761581 | 2 |
| (C2×D79)⋊C32 | 2 |
| C79×#1416 | 2 |
| #13716 | 79 |