Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
644 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 211 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×Dic42 | C2 | semidirect |
| 3. C2×C3×C7×C4⋊C4 | C2 | semidirect |
| 5. C2×C4⋊Dic21 | C2 | semidirect |
| 6. #10621380 | C2 | direct (N × H) |
| 16. C2×Dic42 | C22 | semidirect |
| 17. C3×C7×C4⋊C4 | C22 | semidirect |
| 19. C4⋊Dic21 | C22 | semidirect |
| 22. C2×C7×C4⋊C4 | D3 | semidirect |
| 30. C22×D21 | Q8 | semidirect |
| 51. C7×C4⋊C4 | C2×D3 | semidirect |
| 56. C2×C3×C4⋊C4 | D7 | semidirect |
| 67. C2×D21 | C2×Q8 | semidirect |
| 97. C3×C4⋊C4 | C2×D7 | semidirect |
| 100. C2×C3×C7 | C22⋊Q8 | semidirect |
| 109. C2×C4⋊C4 | D21 | semidirect |
| 138. C3×C7 | C2×C22⋊Q8 | semidirect |
| 149. C4⋊C4 | C2×D21 | semidirect |
| 151. C2×C7 | #897 | semidirect |
| 183. C7 | C2×#897 | semidirect |
| 184. C2×C3 | #6460 | semidirect |
| 201. C3 | C2×#6460 | semidirect |
| 203. C2 | #10621380 | 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×Dic42 | 2 |
| C2×C3×C7×C4⋊C4 | 2 |
| C2×#66631 | 2 |
| C2×C4⋊Dic21 | 2 |
| #10621380 | 2 |
| C2×#6460 | 3 |
| C2×#897 | 7 |