Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
376 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 376 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 |
|---|---|---|
| 12. #19098671 | C4 | semidirect |
| 139. C79 | #12827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772269 | 2 |
| #23765166 | 2 |
| C2×#19098378 | 2 |
| #23765119 | 2 |
| #23761514 | 2 |
| #23761501 | 2 |
| C79×#1833 | 2 |
| #12827 | 79 |