Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
256 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 77 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×#66633 | C2 | semidirect |
| 3. C4×Dic42 | C2 | semidirect |
| 4. #10620671 | C2 | semidirect |
| 5. C4⋊(C3⋊(C7⋊C8)) | C2 | semidirect |
| 34. Dic42 | D4 | semidirect |
| 56. C3×C4×C7 | SD16 | semidirect |
| 99. C4×C7 | #214 | semidirect |
| 117. C3×C7 | #460 | semidirect |
| 137. C3×C4 | #1142 | semidirect |
| 155. C7 | #5075 | semidirect |
| 167. C4 | #66633 | semidirect |
| 170. C3 | #89847 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#127 | 2 |
| C2×#66633 | 2 |
| C4×Dic42 | 2 |
| #10620671 | 2 |
| C4⋊(C3⋊(C7⋊C8)) | 2 |
| #89847 | 3 |
| #5075 | 7 |