Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
272 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#19149614 | C2 | semidirect |
| 4. #26011256 | C2 | semidirect |
| 5. #341×C173 | C2 | semidirect |
| 64. C173 | #1811 | semidirect |
| 70. #341 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583809 | 2 |
| C2×#19149614 | 2 |
| #26011454 | 2 |
| #26011256 | 2 |
| #341×C173 | 2 |
| #1811 | 173 |