Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
286 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26011533 | C2 | semidirect |
| 4. #26011357 | C2 | semidirect |
| 5. #26011259 | C2 | semidirect |
| 6. #26011251 | C2 | semidirect |
| 25. #104×C173 | C4 | semidirect |
| 54. M16×C173 | C2×C4 | semidirect |
| 57. C42×C173 | C2×C4 | semidirect |
| 111. C173 | #1860 | semidirect |
| 134. #104 | Dic173 | semidirect |
| 154. M16 | C2×Dic173 | semidirect |
| 169. C42 | C2×Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011974 | 2 |
| #26011533 | 2 |
| #26011492 | 2 |
| #26011357 | 2 |
| #26011259 | 2 |
| #26011251 | 2 |
| C2×#104×C173 | 2 |
| #1860 | 173 |