Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
516 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 192 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. C2×#66569 | C2 | direct (N × H) |
| 14. #66569 | C22 | direct (N × H) |
| 43. C22×C3×C7 | Q16 | semidirect |
| 69. C2×C3×C7 | C2×Q16 | semidirect |
| 75. C22×C7 | #216 | semidirect |
| 91. C3×C7 | C22×Q16 | semidirect |
| 101. C2×C7 | C2×#216 | semidirect |
| 103. C22×C3 | #1144 | semidirect |
| 119. C7 | C22×#216 | semidirect |
| 120. C2×C3 | C2×#1144 | semidirect |
| 122. C22 | #66569 | direct (N × H) |
| 128. C3 | C22×#1144 | semidirect |
| 129. C2 | C2×#66569 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Dic6 | 2 |
| C22×C3×Dic14 | 2 |
| C22×C3⋊(C7⋊C8) | 2 |
| C2×#66569 | 2 |
| C22×#1144 | 3 |
| C22×#216 | 7 |