Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
684 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 168 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×D21⋊C4 | C2 | semidirect |
| 3. C2×C7×Dic3⋊C4 | C2 | semidirect |
| 4. C2×C3×Dic7⋊C4 | C2 | semidirect |
| 5. C2×#66575 | C2 | semidirect |
| 6. C2×#66575 | C2 | semidirect |
| 7. C2×#66575 | C2 | semidirect |
| 8. #10620995 | C2 | direct (N × H) |
| 20. C2×D21⋊C4 | C22 | semidirect |
| 21. C7×Dic3⋊C4 | C22 | semidirect |
| 22. C3×Dic7⋊C4 | C22 | semidirect |
| 23. #66575 | C22 | semidirect |
| 24. #66575 | C22 | semidirect |
| 25. #66575 | C22 | semidirect |
| 32. C2×Dic7⋊C4 | D3 | semidirect |
| 71. Dic7⋊C4 | C2×D3 | semidirect |
| 78. C2×Dic3⋊C4 | D7 | semidirect |
| 134. Dic3⋊C4 | C2×D7 | semidirect |
| 135. C2×C3×C7 | #123 | semidirect |
| 187. C3×C7 | C2×#123 | semidirect |
| 204. C2×C7 | #894 | semidirect |
| 248. C7 | C2×#894 | semidirect |
| 249. C2×C3 | #6457 | semidirect |
| 272. C3 | C2×#6457 | semidirect |
| 275. C2 | #10620995 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D84 | 2 |
| C22×D21⋊C4 | 2 |
| C2×C7×Dic3⋊C4 | 2 |
| C2×C3×Dic7⋊C4 | 2 |
| C2×#66575 | 2 |
| #10620995 | 2 |
| C2×#6457 | 3 |
| C2×#894 | 7 |