Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
300 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 96 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×C7×#208 | C2 | semidirect |
| 3. C2×C3×#1136 | C2 | semidirect |
| 4. #10620498 | C2 | semidirect |
| 5. #10620495 | C2 | semidirect |
| 24. C2×#1136 | D3 | semidirect |
| 64. C2×#208 | D7 | semidirect |
| 153. C3×C7 | #413 | semidirect |
| 204. C7 | #5132 | semidirect |
| 221. C3 | #89904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66728 | 2 |
| C2×C7×#208 | 2 |
| C2×C3×#1136 | 2 |
| #10620498 | 2 |
| #10620495 | 2 |
| #89904 | 3 |
| #5132 | 7 |