Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
220 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 14. Dic84 | C4 | semidirect |
| 49. Dic21 | Q16 | semidirect |
| 92. C3×C7 | C4×Q16 | semidirect |
| 120. C7 | #4873 | semidirect |
| 131. C3 | #89645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic84 | 2 |
| #10621370 | 2 |
| C3×C7×#107 | 2 |
| C8×Dic21 | 2 |
| #10620649 | 2 |
| #89645 | 3 |
| #4873 | 7 |