Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
676 conjugacy classes of subgroups; only the 352 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 352 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×C3⋊(C7⋊C8) | C2 | semidirect |
| 3. C22×C7×C3⋊C8 | C2 | semidirect |
| 4. C2×D7×C3⋊C8 | C2 | direct (N × H) |
| 11. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 12. C2×C7×C3⋊C8 | C22 | semidirect |
| 13. D7×C3⋊C8 | C22 | direct (N × H) |
| 20. C22×C3×D7 | C8 | semidirect |
| 27. C3⋊(C7⋊C8) | C23 | semidirect |
| 28. C7×C3⋊C8 | C23 | semidirect |
| 40. C22×C3⋊C8 | D7 | direct (N × H) |
| 41. C22×C3×C7 | C2×C8 | semidirect |
| 43. C2×C3×D7 | C2×C8 | semidirect |
| 50. C22×D7 | C3⋊C8 | direct (N × H) |
| 66. C2×C3⋊C8 | C2×D7 | direct (N × H) |
| 67. C2×C3×C7 | C22×C8 | semidirect |
| 69. C3×D7 | C22×C8 | semidirect |
| 74. C22×C7 | C2×C3⋊C8 | semidirect |
| 76. C2×D7 | C2×C3⋊C8 | direct (N × H) |
| 90. C3⋊C8 | C22×D7 | direct (N × H) |
| 91. C3×C7 | C23×C8 | semidirect |
| 100. C2×C7 | C22×C3⋊C8 | semidirect |
| 102. D7 | C22×C3⋊C8 | direct (N × H) |
| 105. C22×C3 | C8×D7 | semidirect |
| 120. C7 | C23×C3⋊C8 | semidirect |
| 122. C2×C3 | C2×C8×D7 | semidirect |
| 126. C22 | D7×C3⋊C8 | direct (N × H) |
| 131. C3 | C22×C8×D7 | semidirect |
| 133. C2 | C2×D7×C3⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×D7 | 2 |
| C22×C3⋊(C7⋊C8) | 2 |
| C22×C7×C3⋊C8 | 2 |
| C2×D7×C3⋊C8 | 2 |
| C22×C8×D7 | 3 |
| C23×C3⋊C8 | 7 |