Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
348 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 107 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×#19149610 | C2 | semidirect |
| 3. C2×#19149602 | C2 | semidirect |
| 5. C2×C4×#13063436 | C2 | semidirect |
| 6. #26011397 | C2 | semidirect |
| 11. C2×#14583814 | C4 | semidirect |
| 66. #13063436 | C22⋊C4 | semidirect |
| 81. C2×C4×C173 | SD16 | semidirect |
| 112. C173 | #1968 | semidirect |
| 192. C2×C4 | #14583814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583814 | 2 |
| C2×#19149610 | 2 |
| C2×#19149602 | 2 |
| C2×#19149600 | 2 |
| C2×C4×#13063436 | 2 |
| #26011397 | 2 |
| #390×C173 | 2 |
| #1968 | 173 |