Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
148 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 47 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. C2×#19149620 | C2 | semidirect |
| 2. #26011908 | C2 | semidirect |
| 3. #26011761 | C2 | semidirect |
| 4. #26011320 | C2 | semidirect |
| 5. #26011304 | C2 | semidirect |
| 6. #26011303 | C2 | semidirect |
| 7. #472×C173 | C2 | semidirect |
| 73. C173 | #2221 | semidirect |
| 78. #472 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149620 | 2 |
| #26011908 | 2 |
| #26011761 | 2 |
| #26011320 | 2 |
| #26011304 | 2 |
| #26011303 | 2 |
| #472×C173 | 2 |
| #2221 | 173 |