Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
406 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23762158 | C2 | semidirect |
| 4. #23762088 | C2 | semidirect |
| 5. #23761854 | C2 | semidirect |
| 7. C79×#1292 | C2 | semidirect |
| 188. #1292 | D79 | semidirect |
| 189. C79 | #10461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773199 | 2 |
| #23763389 | 2 |
| #23762158 | 2 |
| #23762088 | 2 |
| #23761854 | 2 |
| C2×#19098290 | 2 |
| C79×#1292 | 2 |
| #10461 | 79 |