Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
676 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 382 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×C3×C22⋊Dic7 | C2 | semidirect |
| 3. C3×D4×Dic7 | C2 | semidirect |
| 4. C3×#6489 | C2 | semidirect |
| 5. #90489 | C3 | direct (N × H) |
| 7. C2×C3×C7×D4 | C4 | semidirect |
| 10. C22×C3×Dic7 | C22 | semidirect |
| 12. C3×C22⋊Dic7 | C22 | semidirect |
| 13. C3×C4⋊Dic7 | C22 | semidirect |
| 14. C3×C4×Dic7 | C22 | semidirect |
| 16. C2×C22⋊Dic7 | C2×C3 | semidirect |
| 17. D4×Dic7 | C2×C3 | semidirect |
| 18. #6489 | C2×C3 | semidirect |
| 21. C23×C3×C7 | C2×C4 | semidirect |
| 24. C3×C7×D4 | C2×C4 | semidirect |
| 25. C2×C3×C4×C7 | C2×C4 | semidirect |
| 30. C2×C7×D4 | C3×C4 | semidirect |
| 33. C22×Dic7 | C22×C3 | semidirect |
| 35. C22⋊Dic7 | C22×C3 | semidirect |
| 36. C4⋊Dic7 | C22×C3 | semidirect |
| 37. C4×Dic7 | C22×C3 | semidirect |
| 52. C23×C7 | C2×C3×C4 | semidirect |
| 55. C7×D4 | C2×C3×C4 | semidirect |
| 56. C2×C4×C7 | C2×C3×C4 | semidirect |
| 61. C2×C3×D4 | Dic7 | semidirect |
| 86. C23×C3 | C2×Dic7 | semidirect |
| 89. C3×D4 | C2×Dic7 | semidirect |
| 92. C2×C3×C4 | C2×Dic7 | semidirect |
| 94. C3×C7 | #518 | semidirect |
| 96. C2×D4 | C3×Dic7 | semidirect |
| 117. C23 | C2×C3×Dic7 | semidirect |
| 120. D4 | C2×C3×Dic7 | semidirect |
| 123. C2×C4 | C2×C3×Dic7 | semidirect |
| 125. C7 | C3×#518 | semidirect |
| 138. C3 | #90489 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×D4 | 2 |
| C2×C3×C22⋊Dic7 | 2 |
| C3×D4×Dic7 | 2 |
| C3×#6489 | 2 |
| #90489 | 3 |
| C3×#518 | 7 |