Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
404 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 2. C22×C3⋊(C7⋊C8) | C2 | semidirect |
| 3. C2×C3×C4⋊Dic7 | C2 | semidirect |
| 4. #10620501 | C2 | direct (N × H) |
| 10. C2×C7×D12 | C4 | semidirect |
| 14. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 16. C3×C4⋊Dic7 | C22 | semidirect |
| 18. C2×C4⋊Dic7 | D3 | semidirect |
| 33. C7×D12 | C2×C4 | semidirect |
| 45. C4⋊Dic7 | C2×D3 | semidirect |
| 85. C2×D12 | Dic7 | semidirect |
| 91. C2×C3×C7 | #102 | semidirect |
| 125. D12 | C2×Dic7 | semidirect |
| 127. C3×C7 | C2×#102 | semidirect |
| 140. C2×C7 | #809 | semidirect |
| 171. C7 | C2×#809 | semidirect |
| 172. C2×C3 | #6406 | semidirect |
| 189. C3 | C2×#6406 | semidirect |
| 191. C2 | #10620501 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D12 | 2 |
| C22×C3⋊(C7⋊C8) | 2 |
| C2×C3×C4⋊Dic7 | 2 |
| #10620501 | 2 |
| C2×#6406 | 3 |
| C2×#809 | 7 |