Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 72 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×C7×#239 | C2 | semidirect |
| 2. C2×C3×#1143 | C2 | semidirect |
| 3. #10621018 | C2 | semidirect |
| 4. C2×#66560 | C2 | semidirect |
| 5. #10620674 | C2 | semidirect |
| 6. #10620502 | C2 | semidirect |
| 7. (C2×D3)⋊(C7⋊C8) | C2 | semidirect |
| 25. C2×#1143 | D3 | semidirect |
| 36. C3×C7×Q8 | D4 | semidirect |
| 43. C7×D12 | D4 | semidirect |
| 67. C2×#239 | D7 | semidirect |
| 94. C7×Q8 | #67 | semidirect |
| 157. C3×Q8 | C22⋊D7 | semidirect |
| 167. D12 | C22⋊D7 | semidirect |
| 173. C3×C7 | #449 | semidirect |
| 214. Q8 | #4245 | semidirect |
| 230. C7 | #5172 | semidirect |
| 252. C3 | #90010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#239 | 2 |
| C2×C3×#1143 | 2 |
| #10621018 | 2 |
| C2×#66560 | 2 |
| #10620674 | 2 |
| #10620502 | 2 |
| (C2×D3)⋊(C7⋊C8) | 2 |
| #90010 | 3 |
| #5172 | 7 |