Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
376 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 90 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. C2×C3×#1142 | C2 | semidirect |
| 3. C2×C3×#1132 | C2 | semidirect |
| 4. C3×#6460 | C2 | semidirect |
| 5. C3×C7×#102 | C2 | semidirect |
| 6. C3×(C2×D7)⋊C8 | C2 | semidirect |
| 7. C3×#6383 | C2 | semidirect |
| 8. #89548 | C3 | direct (N × H) |
| 16. C2×C3×Dic14 | C22 | semidirect |
| 17. C2×C3×C7×C8 | C22 | semidirect |
| 18. C3×C7×C4⋊C4 | C22 | semidirect |
| 22. C2×C3×C7⋊C8 | C22 | semidirect |
| 25. C2×#1142 | C2×C3 | semidirect |
| 26. C2×#1132 | C2×C3 | semidirect |
| 27. #6460 | C2×C3 | semidirect |
| 28. C7×#102 | C2×C3 | semidirect |
| 29. (C2×D7)⋊C8 | C2×C3 | semidirect |
| 30. #6383 | C2×C3 | semidirect |
| 60. C2×Dic14 | C22×C3 | semidirect |
| 61. C2×C7×C8 | C22×C3 | semidirect |
| 62. C7×C4⋊C4 | C22×C3 | semidirect |
| 66. C2×C7⋊C8 | C22×C3 | semidirect |
| 73. C3×#102 | D7 | semidirect |
| 85. C2×C3×D7 | SD16 | semidirect |
| 124. C2×C3×C8 | C2×D7 | semidirect |
| 126. C3×C4⋊C4 | C2×D7 | semidirect |
| 139. #102 | C3×D7 | semidirect |
| 151. C2×D7 | C3×SD16 | semidirect |
| 178. C3×C7 | #450 | semidirect |
| 190. C2×C8 | C2×C3×D7 | semidirect |
| 192. C4⋊C4 | C2×C3×D7 | semidirect |
| 237. C7 | C3×#450 | semidirect |
| 260. C3 | #89548 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×D7 | 2 |
| C2×C3×#1142 | 2 |
| C2×C3×#1132 | 2 |
| C3×#6460 | 2 |
| C3×C7×#102 | 2 |
| C3×(C2×D7)⋊C8 | 2 |
| C3×#6383 | 2 |
| #89548 | 3 |
| C3×#450 | 7 |