Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
596 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 596 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 |
|---|---|---|
| 2. C22×C7×Dic6 | C2 | semidirect |
| 3. C22×C3×C7⋊C8 | C2 | semidirect |
| 4. C2×#66568 | C2 | direct (N × H) |
| 12. C2×C7×Dic6 | C22 | semidirect |
| 13. C2×C3×C7⋊C8 | C22 | semidirect |
| 14. #66568 | C22 | direct (N × H) |
| 18. C22×C7⋊C8 | D3 | semidirect |
| 29. C7×Dic6 | C23 | semidirect |
| 30. C3×C7⋊C8 | C23 | semidirect |
| 39. C2×C7⋊C8 | C2×D3 | semidirect |
| 41. C22×Dic6 | D7 | semidirect |
| 44. C22×C3×C7 | SD16 | semidirect |
| 62. C7⋊C8 | C22×D3 | semidirect |
| 69. C2×Dic6 | C2×D7 | semidirect |
| 72. C2×C3×C7 | C2×SD16 | semidirect |
| 79. C22×C7 | #204 | semidirect |
| 95. Dic6 | C22×D7 | semidirect |
| 97. C3×C7 | C22×SD16 | semidirect |
| 107. C2×C7 | C2×#204 | semidirect |
| 110. C22×C3 | #1143 | semidirect |
| 128. C7 | C22×#204 | semidirect |
| 129. C2×C3 | C2×#1143 | semidirect |
| 134. C22 | #66568 | direct (N × H) |
| 139. C3 | C22×#1143 | semidirect |
| 141. C2 | C2×#66568 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D84 | 2 |
| C22×C7×Dic6 | 2 |
| C22×C3×C7⋊C8 | 2 |
| C2×#66568 | 2 |
| C22×#1143 | 3 |
| C22×#204 | 7 |