Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 76 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. #10621352 | C2 | semidirect |
| 4. C3×C4⋊(C7⋊C8) | C2 | semidirect |
| 5. #10620510 | C2 | semidirect |
| 21. C4⋊(C7⋊C8) | D3 | semidirect |
| 55. C3×C4×C7 | SD16 | semidirect |
| 98. C4×C7 | #204 | semidirect |
| 114. C3×C7 | #461 | semidirect |
| 134. C3×C4 | #1142 | semidirect |
| 151. C7 | #4841 | semidirect |
| 163. C4 | #66567 | semidirect |
| 166. C3 | #89791 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621352 | 2 |
| C4×C7×D12 | 2 |
| C2×#66567 | 2 |
| C3×C4⋊(C7⋊C8) | 2 |
| #10620510 | 2 |
| #89791 | 3 |
| #4841 | 7 |