Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
600 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 349 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×#19149612 | C2 | direct (N × H) |
| 6. C22×#13063436 | C4 | semidirect |
| 10. #19149612 | C22 | direct (N × H) |
| 17. C2×#13063436 | C2×C4 | semidirect |
| 32. #13063436 | C22×C4 | semidirect |
| 44. C22×C173 | #107 | semidirect |
| 54. C2×C173 | C2×#107 | semidirect |
| 58. C173 | C22×#107 | semidirect |
| 103. C22 | #19149612 | direct (N × H) |
| 113. C2 | C2×#19149612 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#13063436 | 2 |
| C22×C4⋊Dic173 | 2 |
| C2×#19149612 | 2 |
| C22×C4⋊C4×C173 | 2 |
| C22×#107 | 173 |