Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 92 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. #10620651 | C2 | semidirect |
| 3. C7×#812 | C2 | semidirect |
| 4. #10620469 | C2 | semidirect |
| 5. D7×C3⋊C16 | C2 | semidirect |
| 14. C3⋊(C7⋊C16) | C22 | semidirect |
| 15. C7×C3⋊C16 | C22 | semidirect |
| 45. #812 | D7 | direct (N × H) |
| 75. C3⋊C16 | C2×D7 | semidirect |
| 79. C3×D7 | M32 | semidirect |
| 104. C3×C7 | C2×M32 | semidirect |
| 117. D7 | #812 | direct (N × H) |
| 137. C7 | C2×#812 | semidirect |
| 150. C3 | D7×M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C8×D7 | 2 |
| #10620651 | 2 |
| C7×#812 | 2 |
| #10620469 | 2 |
| D7×C3⋊C16 | 2 |
| D7×M32 | 3 |
| C2×#812 | 7 |