Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
200 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 54 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. C2×#66635 | C2 | semidirect |
| 5. C3×#6410 | C2 | semidirect |
| 6. #10620527 | C2 | semidirect |
| 7. #10620498 | C2 | semidirect |
| 28. #6410 | D3 | semidirect |
| 142. C3×C7 | #473 | semidirect |
| 184. C7 | #4755 | semidirect |
| 195. C3 | #89976 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66635 | 2 |
| C7×#942 | 2 |
| #10620884 | 2 |
| #10620850 | 2 |
| C3×#6410 | 2 |
| #10620527 | 2 |
| #10620498 | 2 |
| #89976 | 3 |
| #4755 | 7 |