Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
364 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 73 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. #23763574 | C2 | semidirect |
| 4. #23762015 | C2 | semidirect |
| 6. #23761310 | C2 | semidirect |
| 7. C79×#1559 | C2 | semidirect |
| 157. #1559 | D79 | semidirect |
| 162. C79 | #10526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774783 | 2 |
| #23763574 | 2 |
| #23762120 | 2 |
| #23762015 | 2 |
| #23762012 | 2 |
| #23761310 | 2 |
| C79×#1559 | 2 |
| #10526 | 79 |