Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
106 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 25 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 |
|---|---|---|
| 1. #26011290 | C2 | semidirect |
| 2. #26011240 | C2 | semidirect |
| 51. C173 | #1405 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011290 | 2 |
| #26011240 | 2 |
| #456×C173 | 2 |
| #1405 | 173 |