Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26011965 | C2 | semidirect |
| 3. #26011508 | C2 | semidirect |
| 4. C2×#19149595 | C2 | semidirect |
| 5. #26011248 | C2 | semidirect |
| 6. #26011247 | C2 | semidirect |
| 7. #421×C173 | C2 | semidirect |
| 10. #19149675 | C4 | semidirect |
| 11. #19149668 | C4 | semidirect |
| 43. C4×Dic173 | C2×C4 | semidirect |
| 44. C4×Dic173 | D4 | semidirect |
| 49. C2×Q8×C173 | C2×C4 | semidirect |
| 51. C2×D4×C173 | C2×C4 | semidirect |
| 59. C42×C173 | D4 | semidirect |
| 116. C173 | #1911 | semidirect |
| 121. #421 | D173 | semidirect |
| 147. C2×Q8 | C4×D173 | semidirect |
| 156. C2×D4 | C4×D173 | semidirect |
| 176. C42 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012055 | 2 |
| #26011965 | 2 |
| #26011508 | 2 |
| C2×#19149595 | 2 |
| #26011248 | 2 |
| #26011247 | 2 |
| #421×C173 | 2 |
| #1911 | 173 |