Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
334 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #23763519 | C2 | semidirect |
| 3. #23762176 | C2 | semidirect |
| 6. #23761228 | C2 | semidirect |
| 7. C79×#1570 | C2 | semidirect |
| 132. #1570 | D79 | semidirect |
| 136. C79 | #10665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764231 | 2 |
| #23763519 | 2 |
| #23762176 | 2 |
| #23761800 | 2 |
| #23761798 | 2 |
| #23761228 | 2 |
| C79×#1570 | 2 |
| #10665 | 79 |