Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
644 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 200 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×C7×Dic6 | C2 | semidirect |
| 3. C2×C3×C4⋊Dic7 | C2 | semidirect |
| 4. C2×Dic7⋊Dic3 | C2 | semidirect |
| 6. #10620945 | C2 | direct (N × H) |
| 15. C2×C7×Dic6 | C22 | semidirect |
| 17. C3×C4⋊Dic7 | C22 | semidirect |
| 18. Dic7⋊Dic3 | C22 | semidirect |
| 24. C2×C4⋊Dic7 | D3 | semidirect |
| 30. C22×D21 | Q8 | semidirect |
| 52. C4⋊Dic7 | C2×D3 | semidirect |
| 55. C22×Dic6 | D7 | semidirect |
| 67. C2×D21 | C2×Q8 | semidirect |
| 96. C2×Dic6 | C2×D7 | semidirect |
| 100. C2×C3×C7 | C22⋊Q8 | semidirect |
| 138. C3×C7 | C2×C22⋊Q8 | semidirect |
| 151. C2×C7 | #897 | semidirect |
| 183. C7 | C2×#897 | semidirect |
| 184. C2×C3 | #6509 | semidirect |
| 201. C3 | C2×#6509 | semidirect |
| 203. C2 | #10620945 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D21 | 2 |
| C22×C7×Dic6 | 2 |
| C2×C3×C4⋊Dic7 | 2 |
| C2×Dic7⋊Dic3 | 2 |
| C2×#66575 | 2 |
| #10620945 | 2 |
| C2×#6509 | 3 |
| C2×#897 | 7 |