Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 1. C2×#19149710 | C2 | semidirect |
| 2. C2×M16×D173 | C2 | semidirect |
| 4. C2×#19149655 | C2 | semidirect |
| 5. #26011748 | C2 | semidirect |
| 6. #26011740 | C2 | semidirect |
| 7. #26011731 | C2 | semidirect |
| 8. #26011723 | C2 | semidirect |
| 9. #26011534 | C2 | semidirect |
| 10. #26011493 | C2 | semidirect |
| 11. #419×C173 | C2 | semidirect |
| 15. C2×#14583816 | C22 | semidirect |
| 16. C2×#14583813 | C22 | semidirect |
| 36. #19149612 | C22 | semidirect |
| 37. #19149610 | C22 | semidirect |
| 38. #19149604 | C22 | semidirect |
| 39. #19149601 | C22 | semidirect |
| 43. #103×C173 | C22 | semidirect |
| 44. #103×C173 | C22 | semidirect |
| 64. #14583810 | D4 | semidirect |
| 145. C2×D173 | #137 | semidirect |
| 163. C173 | #3056 | semidirect |
| 174. #419 | D173 | semidirect |
| 206. #103 | C2×D173 | semidirect |
| 207. #103 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149710 | 2 |
| C2×M16×D173 | 2 |
| #26012003 | 2 |
| C2×#19149655 | 2 |
| #26011748 | 2 |
| #26011740 | 2 |
| #26011731 | 2 |
| #26011723 | 2 |
| #26011534 | 2 |
| #26011493 | 2 |
| #419×C173 | 2 |
| #3056 | 173 |