Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
260 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 174 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 |
|---|---|---|
| 3. C3×#6392 | C2 | direct (N × H) |
| 4. C2×#6392 | C3 | direct (N × H) |
| 7. C2×C3×C7×C8 | C4 | semidirect |
| 13. #6392 | C2×C3 | direct (N × H) |
| 22. C3×C7×C8 | C2×C4 | semidirect |
| 25. C2×C7×C8 | C3×C4 | semidirect |
| 48. C7×C8 | C2×C3×C4 | semidirect |
| 51. C2×C3×C8 | Dic7 | semidirect |
| 55. C2×C3×C7 | #107 | semidirect |
| 77. C3×C8 | C2×Dic7 | semidirect |
| 78. C3×C7 | C2×#107 | semidirect |
| 81. C2×C8 | C3×Dic7 | semidirect |
| 85. C2×C7 | C3×#107 | semidirect |
| 104. C8 | C2×C3×Dic7 | semidirect |
| 105. C7 | C2×C3×#107 | semidirect |
| 106. C2×C3 | #6392 | direct (N × H) |
| 118. C3 | C2×#6392 | direct (N × H) |
| 119. C2 | C3×#6392 | 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 |
| C2×C3×C4⋊Dic7 | 2 |
| C3×#6392 | 2 |
| C2×#6392 | 3 |
| C2×C3×#107 | 7 |