Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 78 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×#66559 | C2 | semidirect |
| 3. C2×D21⋊C8 | C2 | semidirect |
| 4. C7×C4⋊(C3⋊C8) | C2 | semidirect |
| 5. C3×#6377 | C2 | semidirect |
| 6. #10620492 | C2 | semidirect |
| 7. #10620492 | C2 | semidirect |
| 28. #6377 | D3 | semidirect |
| 43. C3×C7⋊C8 | D4 | semidirect |
| 65. C4⋊(C3⋊C8) | D7 | semidirect |
| 72. C2×D21 | M16 | semidirect |
| 95. C7⋊C8 | D12 | semidirect |
| 150. C3×C7 | #435 | semidirect |
| 198. C7 | #4706 | semidirect |
| 217. C3 | #89608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D84 | 2 |
| C2×#66559 | 2 |
| C2×D21⋊C8 | 2 |
| C7×C4⋊(C3⋊C8) | 2 |
| C3×#6377 | 2 |
| #10620492 | 2 |
| #89608 | 3 |
| #4706 | 7 |