Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
596 conjugacy classes of subgroups; only the 430 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 430 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. C7×Q8×Dic3 | C2 | direct (N × H) |
| 6. C2×C3×C7×Q8 | C4 | semidirect |
| 17. C2×Q8×Dic3 | C7 | direct (N × H) |
| 19. C3×C7×Q8 | C2×C4 | semidirect |
| 23. C2×C7×Dic3 | Q8 | direct (N × H) |
| 26. C2×C7×Q8 | Dic3 | direct (N × H) |
| 34. Q8×Dic3 | C2×C7 | direct (N × H) |
| 43. C7×Dic3 | C2×Q8 | direct (N × H) |
| 46. C7×Q8 | C2×Dic3 | direct (N × H) |
| 53. C2×C3×Q8 | C4×C7 | semidirect |
| 60. C2×C3×C7 | C4×Q8 | semidirect |
| 76. C3×Q8 | C2×C4×C7 | semidirect |
| 80. C2×Dic3 | C7×Q8 | direct (N × H) |
| 83. C3×C7 | C2×C4×Q8 | semidirect |
| 84. C2×Q8 | C7×Dic3 | direct (N × H) |
| 91. C2×C7 | Q8×Dic3 | direct (N × H) |
| 101. Dic3 | C2×C7×Q8 | direct (N × H) |
| 103. Q8 | C2×C7×Dic3 | direct (N × H) |
| 110. C7 | C2×Q8×Dic3 | direct (N × H) |
| 111. C2×C3 | C4×C7×Q8 | semidirect |
| 122. C3 | C2×C4×C7×Q8 | semidirect |
| 123. C2 | C7×Q8×Dic3 | 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×Q8 | 2 |
| C7×Q8×Dic3 | 2 |
| C2×C7×C4⋊Dic3 | 2 |
| C2×C4×C7×Dic3 | 2 |
| C2×C4×C7×Q8 | 3 |
| C2×Q8×Dic3 | 7 |