Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
168 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 88 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. C2×C3⋊(C7⋊C16) | C2 | semidirect |
| 3. C7×#812 | C2 | semidirect |
| 4. #10620469 | C2 | semidirect |
| 5. D7×C3⋊C16 | C2 | semidirect |
| 39. #812 | D7 | semidirect |
| 85. C3×C7 | #504 | semidirect |
| 110. C7 | #5140 | semidirect |
| 119. C3 | #89679 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6464 | 2 |
| C2×C3⋊(C7⋊C16) | 2 |
| C7×#812 | 2 |
| #10620469 | 2 |
| D7×C3⋊C16 | 2 |
| #89679 | 3 |
| #5140 | 7 |