Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
684 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 381 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 |
|---|---|---|
| 7. C4×Dic346 | C4 | direct (N × H) |
| 28. C42×C173 | Q8 | semidirect |
| 29. Dic346 | C42 | direct (N × H) |
| 45. C4×C173 | C4×Q8 | semidirect |
| 51. C173 | C42×Q8 | semidirect |
| 80. C42 | Dic346 | direct (N × H) |
| 99. C4 | C4×Dic346 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic346 | 2 |
| C4×#14583805 | 2 |
| C4×C4⋊Dic173 | 2 |
| C42×Dic173 | 2 |
| C43×C173 | 2 |
| C42×Q8 | 173 |