Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
284 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
| 3. C2×#66564 | C2 | semidirect |
| 4. C4×C3⋊(C7⋊C8) | C2 | semidirect |
| 15. #6432 | D3 | semidirect |
| 25. C3⋊(C7⋊C8) | D4 | semidirect |
| 40. C3×C4×C7 | SD16 | semidirect |
| 69. C4×C7 | #215 | semidirect |
| 80. C3×C7 | #492 | semidirect |
| 95. C3×C4 | #1142 | semidirect |
| 105. C7 | #5085 | semidirect |
| 113. C4 | #66564 | semidirect |
| 115. C3 | #89848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#874 | 2 |
| C3×#6432 | 2 |
| C2×#66564 | 2 |
| C4×C3⋊(C7⋊C8) | 2 |
| #89848 | 3 |
| #5085 | 7 |