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. #10621373 | C2 | semidirect |
| 3. C3×#6450 | C2 | semidirect |
| 4. #10620950 | C2 | semidirect |
| 5. #10620947 | C2 | semidirect |
| 10. #10620898 | C2 | semidirect |
| 11. Dic6×Dic7 | C2 | semidirect |
| 44. #6450 | D3 | semidirect |
| 191. C3×C7 | #541 | semidirect |
| 247. C7 | #5583 | semidirect |
| 266. C3 | #90316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621373 | 2 |
| C7×#897 | 2 |
| C3×#6450 | 2 |
| #10620950 | 2 |
| #10620947 | 2 |
| #10620934 | 2 |
| #10620933 | 2 |
| #10620931 | 2 |
| #10620904 | 2 |
| #10620898 | 2 |
| Dic6×Dic7 | 2 |
| #90316 | 3 |
| #5583 | 7 |