Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
740 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 205 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×D692 | C2 | semidirect |
| 3. #26011394 | C2 | semidirect |
| 4. #26011392 | C2 | semidirect |
| 5. #26011370 | C2 | semidirect |
| 6. #26011367 | C2 | semidirect |
| 7. #26011356 | C2 | semidirect |
| 8. #26011337 | C2 | semidirect |
| 9. C2×C4×D4×C173 | C2 | semidirect |
| 13. #19149675 | C4 | semidirect |
| 33. C2×D692 | C2×C4 | semidirect |
| 36. C2×C22⋊D173 | C2×C4 | semidirect |
| 47. C4×Dic173 | C2×C4 | semidirect |
| 51. C2×D4×C173 | C2×C4 | semidirect |
| 60. C42×C173 | D4 | semidirect |
| 123. C173 | #2328 | semidirect |
| 127. C2×C4×D4 | D173 | semidirect |
| 164. C2×D4 | C4×D173 | semidirect |
| 184. C42 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149675 | 2 |
| C2×C4×D692 | 2 |
| #26011394 | 2 |
| #26011392 | 2 |
| #26011370 | 2 |
| #26011367 | 2 |
| #26011356 | 2 |
| #26011337 | 2 |
| C2×C4×D4×C173 | 2 |
| #2328 | 173 |