Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
532 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 200 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. C22×C7×C3⋊C8 | C2 | semidirect |
| 3. C2×C3×#1136 | C2 | semidirect |
| 4. C2×#66559 | C2 | semidirect |
| 5. #10620853 | C2 | direct (N × H) |
| 6. C2×D21⋊C8 | C2 | semidirect |
| 17. C2×C7×C3⋊C8 | C22 | semidirect |
| 18. C3×#1136 | C22 | semidirect |
| 20. #66559 | C22 | semidirect |
| 21. D21⋊C8 | C22 | semidirect |
| 24. C2×#1136 | D3 | semidirect |
| 54. #1136 | C2×D3 | semidirect |
| 60. C22×C3⋊C8 | D7 | semidirect |
| 100. C2×C3⋊C8 | C2×D7 | semidirect |
| 104. C2×C3×C7 | #131 | semidirect |
| 137. C3×C7 | C2×#131 | semidirect |
| 153. C2×C7 | #907 | semidirect |
| 180. C7 | C2×#907 | semidirect |
| 182. C2×C3 | #6464 | semidirect |
| 194. C3 | C2×#6464 | semidirect |
| 197. C2 | #10620853 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66728 | 2 |
| C22×C7×C3⋊C8 | 2 |
| C2×C3×#1136 | 2 |
| C2×#66559 | 2 |
| #10620853 | 2 |
| C2×D21⋊C8 | 2 |
| C2×#6464 | 3 |
| C2×#907 | 7 |