Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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×C4⋊C4×D173 | C2 | semidirect |
| 3. C2×#19149600 | C2 | semidirect |
| 4. C2×#19149591 | C2 | semidirect |
| 5. #26011254 | C2 | semidirect |
| 6. #26011253 | C2 | semidirect |
| 7. C2×#102×C173 | C2 | semidirect |
| 13. #19149650 | C4 | semidirect |
| 47. C4⋊Dic173 | C2×C4 | semidirect |
| 48. C4⋊Dic173 | D4 | semidirect |
| 57. C2×D4×C173 | C2×C4 | semidirect |
| 64. C4⋊C4×C173 | D4 | semidirect |
| 130. C2×D173 | #102 | semidirect |
| 148. C173 | #1874 | semidirect |
| 153. C2×#102 | D173 | semidirect |
| 185. C2×D4 | C4×D173 | semidirect |
| 212. C4⋊C4 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149650 | 2 |
| C2×C4⋊C4×D173 | 2 |
| C2×#19149600 | 2 |
| C2×#19149591 | 2 |
| #26011254 | 2 |
| #26011253 | 2 |
| C2×#102×C173 | 2 |
| #1874 | 173 |