Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 216 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. C7×#869 | C2 | semidirect |
| 4. C7×#807 | C2 | semidirect |
| 5. C7×C4⋊(C3⋊C8) | C2 | semidirect |
| 21. #5007 | C7 | direct (N × H) |
| 24. C3×C7×D4 | Q8 | semidirect |
| 43. #869 | C2×C7 | semidirect |
| 45. #807 | C2×C7 | semidirect |
| 46. C4⋊(C3⋊C8) | C2×C7 | semidirect |
| 61. C7×D4 | Dic6 | semidirect |
| 99. C3×D4 | C7×Q8 | semidirect |
| 108. C3×C7 | #474 | semidirect |
| 135. D4 | C7×Dic6 | semidirect |
| 143. C7 | #5007 | direct (N × H) |
| 158. C3 | C7×#474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×D4 | 2 |
| C7×#869 | 2 |
| C7×#832 | 2 |
| C7×#807 | 2 |
| C7×C4⋊(C3⋊C8) | 2 |
| C7×#474 | 3 |
| #5007 | 7 |