Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
348 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×#19149589 | C2 | semidirect |
| 4. C2×C4×#13063436 | C2 | semidirect |
| 6. #26011245 | C2 | semidirect |
| 7. #336×C173 | C2 | semidirect |
| 11. C2×#14583809 | C4 | semidirect |
| 16. #19149591 | C4 | semidirect |
| 68. #13063436 | C22⋊C4 | semidirect |
| 72. C2×C4×C173 | M16 | semidirect |
| 104. C173 | #1753 | semidirect |
| 112. #336 | D173 | semidirect |
| 175. C2×C4 | #14583809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583809 | 2 |
| C2×#19149591 | 2 |
| C2×#19149589 | 2 |
| C2×C4×#13063436 | 2 |
| C4×#14583803 | 2 |
| #26011245 | 2 |
| #336×C173 | 2 |
| #1753 | 173 |