Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×#66732 | C2 | semidirect |
| 2. C2×#66634 | C2 | semidirect |
| 3. C2×D168 | C2 | semidirect |
| 4. #10621378 | C2 | semidirect |
| 5. C3×C7×#103 | C2 | semidirect |
| 6. #10620659 | C2 | semidirect |
| 7. #10620648 | C2 | semidirect |
| 28. C7×#103 | D3 | semidirect |
| 36. C3×C7×Q8 | D4 | semidirect |
| 46. D84 | D4 | semidirect |
| 71. C3×#103 | D7 | semidirect |
| 94. C7×Q8 | D12 | semidirect |
| 135. #103 | D21 | semidirect |
| 157. C3×Q8 | D28 | semidirect |
| 173. C3×C7 | #449 | semidirect |
| 214. Q8 | D84 | semidirect |
| 230. C7 | #4810 | semidirect |
| 252. C3 | #89583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66732 | 2 |
| C2×#66634 | 2 |
| C2×D168 | 2 |
| #10621378 | 2 |
| C3×C7×#103 | 2 |
| #10620659 | 2 |
| #10620648 | 2 |
| #89583 | 3 |
| #4810 | 7 |