Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
286 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 61 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. #23765647 | C2 | semidirect |
| 3. #23765451 | C2 | semidirect |
| 5. #23761369 | C2 | semidirect |
| 7. C79×#1363 | C2 | semidirect |
| 144. #1363 | D79 | semidirect |
| 147. C79 | #12351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775973 | 2 |
| #23765647 | 2 |
| #23765451 | 2 |
| #23762890 | 2 |
| #23761369 | 2 |
| #23761357 | 2 |
| C79×#1363 | 2 |
| #12351 | 79 |