Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
152 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #26011314 | C2 | direct (N × H) |
| 12. M32×C173 | C4 | semidirect |
| 14. C2×C16×C173 | C4 | semidirect |
| 28. C16×C173 | C2×C4 | semidirect |
| 54. C2×C173 | #365 | semidirect |
| 56. C173 | C2×#365 | semidirect |
| 65. M32 | Dic173 | semidirect |
| 67. C2×C16 | Dic173 | semidirect |
| 85. C16 | C2×Dic173 | semidirect |
| 111. C2 | #26011314 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149615 | 2 |
| C2×#19149611 | 2 |
| #26011314 | 2 |
| C2×M32×C173 | 2 |
| C2×#365 | 173 |