Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 74 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. C3×#6432 | C2 | semidirect |
| 4. C7×C4⋊(C3⋊C8) | C2 | semidirect |
| 5. #10620506 | C2 | semidirect |
| 19. #6432 | D3 | semidirect |
| 49. C4⋊(C3⋊C8) | D7 | semidirect |
| 55. C3×C4×C7 | SD16 | semidirect |
| 97. C4×C7 | #215 | semidirect |
| 114. C3×C7 | #461 | semidirect |
| 135. C3×C4 | #1132 | semidirect |
| 151. C7 | #5083 | semidirect |
| 163. C4 | #66566 | semidirect |
| 166. C3 | #89613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D84 | 2 |
| C3×#6432 | 2 |
| C2×#66566 | 2 |
| C7×C4⋊(C3⋊C8) | 2 |
| #10620506 | 2 |
| #89613 | 3 |
| #5083 | 7 |