Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
244 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 109 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×#66627 | C2 | semidirect |
| 3. #10620669 | C2 | semidirect |
| 4. C4⋊(C3⋊(C7⋊C8)) | C2 | semidirect |
| 5. C4×C3⋊(C7⋊C8) | C2 | semidirect |
| 32. C3⋊(C7⋊C8) | D4 | semidirect |
| 53. C3×C4×C7 | M16 | semidirect |
| 92. C4×C7 | #208 | semidirect |
| 106. C3×C7 | #436 | semidirect |
| 126. C3×C4 | #1136 | semidirect |
| 140. C7 | #5012 | semidirect |
| 151. C4 | #66627 | semidirect |
| 154. C3 | #89784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×D4 | 2 |
| C2×#66627 | 2 |
| #10620669 | 2 |
| C4⋊(C3⋊(C7⋊C8)) | 2 |
| C4×C3⋊(C7⋊C8) | 2 |
| #89784 | 3 |
| #5012 | 7 |