Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
264 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 102 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×C4×D28 | C2 | semidirect |
| 3. C3×C7×#97 | C2 | semidirect |
| 4. C3×#6395 | C2 | semidirect |
| 5. C3×#6391 | C2 | semidirect |
| 6. #89483 | C3 | direct (N × H) |
| 14. C3×D56 | C4 | semidirect |
| 16. C4×D28 | C2×C3 | semidirect |
| 17. C7×#97 | C2×C3 | semidirect |
| 18. #6395 | C2×C3 | semidirect |
| 19. #6391 | C2×C3 | semidirect |
| 26. C3×D28 | C2×C4 | semidirect |
| 29. C3×C7×C8 | C2×C4 | semidirect |
| 37. D56 | C3×C4 | semidirect |
| 42. C3×#97 | D7 | semidirect |
| 57. D28 | C2×C3×C4 | semidirect |
| 60. C7×C8 | C2×C3×C4 | semidirect |
| 76. #97 | C3×D7 | semidirect |
| 93. C3×C8 | C4×D7 | semidirect |
| 94. C3×C7 | #442 | semidirect |
| 122. C8 | C3×C4×D7 | semidirect |
| 123. C7 | C3×#442 | semidirect |
| 135. C3 | #89483 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D56 | 2 |
| C3×C4×D28 | 2 |
| C3×C7×#97 | 2 |
| C3×#6395 | 2 |
| C3×#6391 | 2 |
| #89483 | 3 |
| C3×#442 | 7 |