Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
644 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 192 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. C22×#4248 | C2 | semidirect |
| 3. C2×C4⋊Dic21 | C2 | semidirect |
| 5. C2×C3×Dic7⋊C4 | C2 | semidirect |
| 6. C2×Dic7⋊Dic3 | C2 | semidirect |
| 8. #10620979 | C2 | direct (N × H) |
| 18. C2×#4248 | C22 | semidirect |
| 21. C4⋊Dic21 | C22 | semidirect |
| 23. C3×Dic7⋊C4 | C22 | semidirect |
| 24. Dic7⋊Dic3 | C22 | semidirect |
| 32. C2×Dic7⋊C4 | D3 | semidirect |
| 38. C22×D3×C7 | Q8 | semidirect |
| 69. Dic7⋊C4 | C2×D3 | semidirect |
| 85. C2×D3×C7 | C2×Q8 | semidirect |
| 128. C2×C3×C7 | C22⋊Q8 | semidirect |
| 158. C22×D3 | Dic14 | semidirect |
| 174. C3×C7 | C2×C22⋊Q8 | semidirect |
| 192. C2×C7 | #897 | semidirect |
| 203. C2×D3 | C2×Dic14 | semidirect |
| 229. C7 | C2×#897 | semidirect |
| 230. C2×C3 | #6441 | semidirect |
| 249. C3 | C2×#6441 | semidirect |
| 251. C2 | #10620979 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4248 | 2 |
| C22×D3×Dic7 | 2 |
| C2×C4⋊Dic21 | 2 |
| C2×C7×(C2×D3)⋊C4 | 2 |
| C2×C3×Dic7⋊C4 | 2 |
| C2×Dic7⋊Dic3 | 2 |
| C2×(C2×D3)⋊Dic7 | 2 |
| #10620979 | 2 |
| C2×#6441 | 3 |
| C2×#897 | 7 |