Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
284 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 4. #10620654 | C2 | semidirect |
| 5. C7×C8×Dic3 | C2 | semidirect |
| 6. #10620489 | C2 | semidirect |
| 7. Dic3×C7⋊C8 | C2 | semidirect |
| 17. C3×#1131 | C4 | semidirect |
| 19. #66557 | C4 | semidirect |
| 36. C3×C7×C8 | C2×C4 | semidirect |
| 37. C3⋊(C7⋊C8) | C2×C4 | semidirect |
| 38. C3×C7⋊C8 | C2×C4 | semidirect |
| 39. C7×C3⋊C8 | C2×C4 | semidirect |
| 50. #1131 | Dic3 | direct (N × H) |
| 57. C8×Dic3 | D7 | semidirect |
| 65. C7×Dic3 | M16 | semidirect |
| 76. C7×C8 | C2×Dic3 | semidirect |
| 78. C7⋊C8 | C2×Dic3 | semidirect |
| 117. C3×C8 | C4×D7 | semidirect |
| 119. C3⋊C8 | C4×D7 | semidirect |
| 120. C3×C7 | C4×M16 | semidirect |
| 142. Dic3 | #1131 | direct (N × H) |
| 154. C8 | Dic3×D7 | semidirect |
| 155. C7 | Dic3×M16 | semidirect |
| 167. C3 | C4×#1131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1131 | 2 |
| C4×Dic3×D7 | 2 |
| C2×#66557 | 2 |
| #10620654 | 2 |
| C7×C8×Dic3 | 2 |
| #10620489 | 2 |
| Dic3×C7⋊C8 | 2 |
| C4×#1131 | 3 |
| Dic3×M16 | 7 |