Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
200 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 2. C2×Dic84 | C2 | semidirect |
| 4. C3×C7×#108 | C2 | semidirect |
| 5. #10620663 | C2 | semidirect |
| 21. C7×#108 | D3 | semidirect |
| 50. C3×#108 | D7 | semidirect |
| 88. #108 | D21 | semidirect |
| 108. C3×C7 | #473 | semidirect |
| 141. C7 | #4896 | semidirect |
| 151. C3 | #89668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621392 | 2 |
| C2×Dic84 | 2 |
| #10621384 | 2 |
| C3×C7×#108 | 2 |
| #10620663 | 2 |
| #89668 | 3 |
| #4896 | 7 |