Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
410 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 1. C7×Q8×A4 | C2 | direct (N × H) |
| 3. C23×C7×Q8 | C3 | semidirect |
| 10. C22×C7×Q8 | C2×C3 | semidirect |
| 12. C2×Q8×A4 | C7 | direct (N × H) |
| 13. C2×C7×A4 | Q8 | direct (N × H) |
| 24. C2×C7×Q8 | A4 | direct (N × H) |
| 29. Q8×A4 | C2×C7 | direct (N × H) |
| 32. C7×A4 | C2×Q8 | direct (N × H) |
| 34. C23×Q8 | C3×C7 | semidirect |
| 38. C23×C7 | C3×Q8 | semidirect |
| 42. C7×Q8 | C2×A4 | direct (N × H) |
| 57. C22×Q8 | C2×C3×C7 | semidirect |
| 66. C22×C7 | C2×C3×Q8 | semidirect |
| 70. C2×A4 | C7×Q8 | direct (N × H) |
| 82. C2×Q8 | C7×A4 | direct (N × H) |
| 90. C2×C7 | Q8×A4 | direct (N × H) |
| 93. A4 | C2×C7×Q8 | direct (N × H) |
| 98. C23 | C3×C7×Q8 | semidirect |
| 102. Q8 | C2×C7×A4 | direct (N × H) |
| 109. C7 | C2×Q8×A4 | direct (N × H) |
| 119. C22 | C2×C3×C7×Q8 | semidirect |
| 127. C2 | C7×Q8×A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×Q8×A4 | 2 |
| C2×C4×C7×A4 | 2 |
| C23×C7×Q8 | 3 |
| C2×C3×C7×Q8 | 4 |
| C2×Q8×A4 | 7 |