Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
384 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 1. #10621352 | C2 | semidirect |
| 2. C7×#870 | C2 | semidirect |
| 6. #10620905 | C2 | semidirect |
| 7. #10620895 | C2 | semidirect |
| 56. #870 | D7 | semidirect |
| 119. C3×C7 | #541 | semidirect |
| 154. C7 | #5518 | semidirect |
| 167. C3 | #90388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621352 | 2 |
| C7×#870 | 2 |
| C3×#6435 | 2 |
| #10620924 | 2 |
| #10620922 | 2 |
| #10620905 | 2 |
| #10620895 | 2 |
| #90388 | 3 |
| #5518 | 7 |