Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 15. #66635 | C4 | semidirect |
| 128. C3×C7 | #441 | semidirect |
| 166. C7 | #5030 | semidirect |
| 179. C3 | #89802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×Q8 | 2 |
| C2×#66635 | 2 |
| C4×Dic42 | 2 |
| #10620674 | 2 |
| #10620649 | 2 |
| #10620647 | 2 |
| #10620642 | 2 |
| #89802 | 3 |
| #5030 | 7 |