Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
392 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 131 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. #10621427 | C2 | semidirect |
| 4. #10621362 | C2 | semidirect |
| 5. #10621361 | C2 | semidirect |
| 6. #10621353 | C2 | semidirect |
| 119. C3×C7 | #563 | semidirect |
| 155. C7 | #5672 | semidirect |
| 167. C3 | #90363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#124 | 2 |
| #10621427 | 2 |
| #10621418 | 2 |
| #10621362 | 2 |
| #10621361 | 2 |
| #10621353 | 2 |
| #90363 | 3 |
| #5672 | 7 |