Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
284 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 3. C3×C4×C7×C8 | C2 | semidirect |
| 4. #10620654 | C2 | semidirect |
| 5. C4×C3⋊(C7⋊C8) | C2 | semidirect |
| 14. #66622 | C4 | direct (N × H) |
| 17. C4×C7×C8 | D3 | semidirect |
| 28. C3×C7×C8 | C2×C4 | semidirect |
| 29. C3⋊(C7⋊C8) | C2×C4 | semidirect |
| 40. C3×C4×C8 | D7 | semidirect |
| 46. C3×C4×C7 | M16 | semidirect |
| 58. C7×C8 | C4×D3 | semidirect |
| 75. C4×C8 | D21 | semidirect |
| 79. C4×C7 | ΓL(1,𝔽25) | semidirect |
| 90. C3×C8 | C4×D7 | semidirect |
| 92. C3×C7 | C4×M16 | semidirect |
| 107. C3×C4 | #1131 | semidirect |
| 119. C8 | C4×D21 | semidirect |
| 120. C7 | C4×ΓL(1,𝔽25) | semidirect |
| 129. C4 | #66622 | direct (N × H) |
| 131. C3 | C4×#1131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66622 | 2 |
| C42×D21 | 2 |
| C3×C4×C7×C8 | 2 |
| #10620654 | 2 |
| C4×C3⋊(C7⋊C8) | 2 |
| C4×#1131 | 3 |
| C4×ΓL(1,𝔽25) | 7 |