Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 149 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. #26011857 | C2 | direct (N × H) |
| 3. C2×#19149599 | C2 | semidirect |
| 4. C2×#19149590 | C2 | semidirect |
| 5. C2×#125×C173 | C2 | semidirect |
| 11. #19149599 | C22 | semidirect |
| 12. #19149590 | C22 | semidirect |
| 14. #125×C173 | C22 | semidirect |
| 59. C2×C173 | #490 | semidirect |
| 63. C173 | C2×#490 | semidirect |
| 66. C2×#125 | D173 | semidirect |
| 76. #125 | C2×D173 | semidirect |
| 124. C2 | #26011857 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149676 | 2 |
| #26011857 | 2 |
| C2×#19149599 | 2 |
| C2×#19149590 | 2 |
| C2×#125×C173 | 2 |
| C2×#490 | 173 |