Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 78 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×#6433 | C2 | semidirect |
| 3. C3×C4×C7×C8 | C2 | semidirect |
| 5. C3×#6390 | C2 | semidirect |
| 6. #89469 | C3 | direct (N × H) |
| 15. #6433 | C2×C3 | semidirect |
| 16. C4×C7×C8 | C2×C3 | semidirect |
| 18. #6390 | C2×C3 | semidirect |
| 39. C3×C4×C8 | D7 | semidirect |
| 70. C4×C8 | C3×D7 | semidirect |
| 86. C3×C7 | #488 | semidirect |
| 112. C7 | C3×#488 | semidirect |
| 123. C3 | #89469 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6438 | 2 |
| C3×#6433 | 2 |
| C3×C4×C7×C8 | 2 |
| C3×#6395 | 2 |
| C3×#6390 | 2 |
| #89469 | 3 |
| C3×#488 | 7 |