Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
376 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 94 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. C3×#6487 | C2 | semidirect |
| 3. C2×C3×#1132 | C2 | semidirect |
| 4. C3×C7×C22⋊C8 | C2 | semidirect |
| 5. C3×#6395 | C2 | semidirect |
| 6. #89503 | C3 | direct (N × H) |
| 12. C2×C3×Dic14 | C22 | semidirect |
| 13. C2×C3×C7×C8 | C22 | semidirect |
| 15. C3×C4⋊Dic7 | C22 | semidirect |
| 19. #6487 | C2×C3 | semidirect |
| 20. C2×#1132 | C2×C3 | semidirect |
| 21. C7×C22⋊C8 | C2×C3 | semidirect |
| 22. #6395 | C2×C3 | semidirect |
| 44. C2×Dic14 | C22×C3 | semidirect |
| 45. C2×C7×C8 | C22×C3 | semidirect |
| 47. C4⋊Dic7 | C22×C3 | semidirect |
| 54. C3×C22⋊C8 | D7 | semidirect |
| 57. C22×C3×C7 | SD16 | semidirect |
| 90. C2×C3×C8 | C2×D7 | semidirect |
| 103. C22⋊C8 | C3×D7 | semidirect |
| 106. C22×C7 | C3×SD16 | semidirect |
| 131. C3×C7 | #450 | semidirect |
| 139. C2×C8 | C2×C3×D7 | semidirect |
| 154. C22×C3 | #1132 | semidirect |
| 175. C7 | C3×#450 | semidirect |
| 187. C22 | C3×#1132 | semidirect |
| 193. C3 | #89503 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D28 | 2 |
| C3×#6487 | 2 |
| C2×C3×#1132 | 2 |
| C3×C7×C22⋊C8 | 2 |
| C3×#6395 | 2 |
| #89503 | 3 |
| C3×#450 | 7 |