Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
278 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23763523 | C2 | semidirect |
| 4. #23761501 | C2 | semidirect |
| 5. #23761496 | C2 | semidirect |
| 6. #23761488 | C2 | semidirect |
| 144. C79 | #13489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765149 | 2 |
| #23764299 | 2 |
| #23763523 | 2 |
| #23761501 | 2 |
| #23761496 | 2 |
| #23761488 | 2 |
| C79×#2138 | 2 |
| #13489 | 79 |