Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 200 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 |
|---|---|---|
| 4. C3⋊C8×Dic7 | C2 | direct (N × H) |
| 8. C2×C3⋊(C7⋊C8) | C4 | semidirect |
| 10. C2×C7×C3⋊C8 | C4 | semidirect |
| 24. C2×C3×Dic7 | C8 | semidirect |
| 26. C3⋊(C7⋊C8) | C2×C4 | semidirect |
| 27. C7×C3⋊C8 | C2×C4 | semidirect |
| 46. C3×Dic7 | C2×C8 | semidirect |
| 53. C2×Dic7 | C3⋊C8 | direct (N × H) |
| 63. C2×C3⋊C8 | Dic7 | direct (N × H) |
| 65. C2×C3×C7 | C4×C8 | semidirect |
| 78. Dic7 | C2×C3⋊C8 | direct (N × H) |
| 87. C3⋊C8 | C2×Dic7 | direct (N × H) |
| 88. C3×C7 | C2×C4×C8 | semidirect |
| 97. C2×C7 | C4×C3⋊C8 | semidirect |
| 116. C7 | C2×C4×C3⋊C8 | semidirect |
| 117. C2×C3 | C8×Dic7 | semidirect |
| 127. C3 | C2×C8×Dic7 | semidirect |
| 128. C2 | C3⋊C8×Dic7 | 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⋊C8) | 2 |
| C22×C7×C3⋊C8 | 2 |
| C2×C3×C4×Dic7 | 2 |
| C3⋊C8×Dic7 | 2 |
| C2×C8×Dic7 | 3 |
| C2×C4×C3⋊C8 | 7 |