Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
376 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 76 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. C7×#924 | C2 | semidirect |
| 3. C2×#66568 | C2 | semidirect |
| 4. C3×C22⋊(C7⋊C8) | C2 | semidirect |
| 5. #10620504 | C2 | semidirect |
| 12. C2×C7×Dic6 | C22 | semidirect |
| 14. C7×C4⋊Dic3 | C22 | semidirect |
| 16. C2×C3×C7⋊C8 | C22 | semidirect |
| 21. C22⋊(C7⋊C8) | D3 | semidirect |
| 49. C2×C7⋊C8 | C2×D3 | semidirect |
| 51. #924 | D7 | semidirect |
| 57. C22×C3×C7 | SD16 | semidirect |
| 88. C2×Dic6 | C2×D7 | semidirect |
| 91. C4⋊Dic3 | C2×D7 | semidirect |
| 106. C22×C7 | #204 | semidirect |
| 131. C3×C7 | #450 | semidirect |
| 150. C22×C3 | #1143 | semidirect |
| 175. C7 | #4731 | semidirect |
| 187. C22 | #66568 | semidirect |
| 193. C3 | #89818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D84 | 2 |
| C7×#924 | 2 |
| C2×#66568 | 2 |
| C3×C22⋊(C7⋊C8) | 2 |
| #10620504 | 2 |
| #89818 | 3 |
| #4731 | 7 |