Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
256 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 1. C3×C4×C7×Q8 | C2 | semidirect |
| 2. C2×#66634 | C2 | semidirect |
| 4. #10620648 | C2 | semidirect |
| 5. C4⋊(C3⋊(C7⋊C8)) | C2 | semidirect |
| 17. C4×C7×Q8 | D3 | semidirect |
| 25. C3×C7×Q8 | D4 | semidirect |
| 46. C3×C4×Q8 | D7 | semidirect |
| 58. C3×C4×C7 | SD16 | semidirect |
| 64. C7×Q8 | D12 | semidirect |
| 91. C4×Q8 | D21 | semidirect |
| 101. C4×C7 | #215 | semidirect |
| 106. C3×Q8 | D28 | semidirect |
| 117. C3×C7 | #460 | semidirect |
| 139. C3×C4 | #1143 | semidirect |
| 144. Q8 | D84 | semidirect |
| 155. C7 | #5027 | semidirect |
| 167. C4 | #66634 | semidirect |
| 170. C3 | #89799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×Q8 | 2 |
| C2×#66634 | 2 |
| #10621357 | 2 |
| #10620648 | 2 |
| C4⋊(C3⋊(C7⋊C8)) | 2 |
| #89799 | 3 |
| #5027 | 7 |