Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
126 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 42 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 |
|---|---|---|
| 54. C173 | #1287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012514 | 2 |
| #26012510 | 2 |
| #26011546 | 2 |
| #1287 | 173 |