Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
474 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 95 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. C22×#14583813 | C2 | semidirect |
| 3. C2×#19149601 | C2 | semidirect |
| 4. C2×#19149600 | C2 | semidirect |
| 5. #26011398 | C2 | semidirect |
| 6. #26011245 | C2 | semidirect |
| 7. C22×SD16×C173 | C2 | semidirect |
| 42. C2×#13063436 | D4 | semidirect |
| 53. C2×Q8×C173 | D4 | semidirect |
| 65. C2×C8×C173 | D4 | semidirect |
| 80. C2×Dic173 | SD16 | semidirect |
| 135. C173 | #2014 | semidirect |
| 138. C22×SD16 | D173 | semidirect |
| 170. C2×Q8 | C22⋊D173 | semidirect |
| 197. C2×C8 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583813 | 2 |
| C2×#19149675 | 2 |
| C2×#19149601 | 2 |
| C2×#19149600 | 2 |
| #26011398 | 2 |
| #26011245 | 2 |
| C22×SD16×C173 | 2 |
| #2014 | 173 |