Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
640 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 389 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×#19149608 | C2 | direct (N × H) |
| 11. #19149608 | C22 | direct (N × H) |
| 16. C22×Dic173 | C8 | semidirect |
| 31. C2×Dic173 | C2×C8 | semidirect |
| 45. C22×C173 | C4⋊C8 | semidirect |
| 54. Dic173 | C22×C8 | semidirect |
| 55. C2×C173 | C2×C4⋊C8 | semidirect |
| 59. C173 | C22×C4⋊C8 | semidirect |
| 105. C22 | #19149608 | direct (N × H) |
| 115. C2 | C2×#19149608 | 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×#19149608 | 2 |
| C23×C8×C173 | 2 |
| C22×C4⋊C8 | 173 |