Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
468 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23761224 | C2 | semidirect |
| 4. #23761222 | C2 | semidirect |
| 174. C79 | #7671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771710 | 2 |
| #23763468 | 2 |
| #23761224 | 2 |
| #23761222 | 2 |
| C4×C22⋊C8×C79 | 2 |
| #7671 | 79 |