Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
188 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 37. C3×C7×C8 | Q8 | semidirect |
| 77. C7×C8 | Dic6 | semidirect |
| 119. C3×C8 | Dic14 | semidirect |
| 122. C3×C7 | #446 | semidirect |
| 157. C8 | Dic42 | semidirect |
| 158. C7 | #4701 | semidirect |
| 171. C3 | #89473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Dic42 | 2 |
| C3×C7×#97 | 2 |
| #10620654 | 2 |
| #10620653 | 2 |
| C8×Dic21 | 2 |
| C4⋊(C3⋊(C7⋊C8)) | 2 |
| #89473 | 3 |
| #4701 | 7 |