Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
284 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 163 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. #10620642 | C2 | semidirect |
| 4. C4×C3⋊(C7⋊C8) | C2 | semidirect |
| 11. #66627 | C4 | direct (N × H) |
| 25. C3⋊(C7⋊C8) | C2×C4 | semidirect |
| 42. C3×C4×C7 | M16 | semidirect |
| 71. C4×C7 | #208 | semidirect |
| 82. C3×C7 | C4×M16 | semidirect |
| 97. C3×C4 | #1136 | semidirect |
| 108. C7 | C4×#208 | semidirect |
| 116. C4 | #66627 | direct (N × H) |
| 119. C3 | C4×#1136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C42×C7 | 2 |
| C2×#66627 | 2 |
| #10620642 | 2 |
| C4×C3⋊(C7⋊C8) | 2 |
| C4×#1136 | 3 |
| C4×#208 | 7 |