Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
| 3. #26011492 | C2 | semidirect |
| 4. C2×#19149595 | C2 | semidirect |
| 5. #26011393 | C2 | semidirect |
| 6. #26011251 | C2 | semidirect |
| 7. C2×#104×C173 | C2 | semidirect |
| 60. M16×C173 | D4 | semidirect |
| 130. C173 | #2037 | semidirect |
| 134. C2×#104 | D173 | semidirect |
| 181. M16 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012055 | 2 |
| #26011533 | 2 |
| #26011492 | 2 |
| C2×#19149595 | 2 |
| #26011393 | 2 |
| #26011251 | 2 |
| C2×#104×C173 | 2 |
| #2037 | 173 |