Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
644 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 184 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 |
| 4. C2×C7×C4⋊Dic3 | C2 | semidirect |
| 5. C2×C3×Dic7⋊C4 | C2 | semidirect |
| 6. C2×Dic7⋊Dic3 | C2 | semidirect |
| 8. #10620981 | C2 | direct (N × H) |
| 18. C2×#4248 | C22 | semidirect |
| 22. C7×C4⋊Dic3 | C22 | semidirect |
| 23. C3×Dic7⋊C4 | C22 | semidirect |
| 24. Dic7⋊Dic3 | C22 | semidirect |
| 32. C2×Dic7⋊C4 | D3 | semidirect |
| 38. C22×D21 | Q8 | semidirect |
| 69. Dic7⋊C4 | C2×D3 | semidirect |
| 76. C2×C4⋊Dic3 | D7 | semidirect |
| 85. C2×D21 | C2×Q8 | semidirect |
| 127. C4⋊Dic3 | C2×D7 | semidirect |
| 128. C2×C3×C7 | C22⋊Q8 | semidirect |
| 174. C3×C7 | C2×C22⋊Q8 | semidirect |
| 191. C2×C7 | #897 | semidirect |
| 229. C7 | C2×#897 | semidirect |
| 230. C2×C3 | #6459 | semidirect |
| 249. C3 | C2×#6459 | semidirect |
| 251. C2 | #10620981 | 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×D21⋊C4 | 2 |
| C2×#66631 | 2 |
| C2×C7×C4⋊Dic3 | 2 |
| C2×C3×Dic7⋊C4 | 2 |
| C2×Dic7⋊Dic3 | 2 |
| C2×#66575 | 2 |
| #10620981 | 2 |
| C2×#6459 | 3 |
| C2×#897 | 7 |