Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
114 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 35 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 |
|---|---|---|
| 2. #26011256 | C2 | semidirect |
| 3. C22⋊C16×C173 | C2 | semidirect |
| 53. C173 | #1349 | semidirect |
| 56. C22⋊C16 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011727 | 2 |
| #26011256 | 2 |
| C22⋊C16×C173 | 2 |
| #1349 | 173 |