Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
588 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 277 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 |
|---|---|---|
| 9. #19149679 | C4 | direct (N × H) |
| 41. C42×C173 | Q8 | semidirect |
| 70. C4×C173 | C4×Q8 | semidirect |
| 71. C4×C173 | C4⋊Q8 | semidirect |
| 79. C173 | C4×C4⋊Q8 | semidirect |
| 121. C42 | Dic346 | semidirect |
| 152. C4 | C4×Dic346 | semidirect |
| 153. C4 | #19149679 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149679 | 2 |
| C2×C4×Dic346 | 2 |
| #26011397 | 2 |
| #26011389 | 2 |
| #26011361 | 2 |
| C4×C4⋊Dic173 | 2 |
| C43×C173 | 2 |
| C4×C4⋊Q8 | 173 |