Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
204 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 86 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×#870 | C2 | semidirect |
| 5. C7×#808 | C2 | semidirect |
| 6. C7×#807 | C2 | semidirect |
| 7. C7×C4⋊(C3⋊C8) | C2 | semidirect |
| 27. #5009 | C7 | direct (N × H) |
| 52. #870 | C2×C7 | semidirect |
| 55. #808 | C2×C7 | semidirect |
| 56. #807 | C2×C7 | semidirect |
| 57. C4⋊(C3⋊C8) | C2×C7 | semidirect |
| 127. C3×C7 | #478 | semidirect |
| 166. C7 | #5009 | direct (N × H) |
| 182. C3 | C7×#478 | 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×#870 | 2 |
| C7×#832 | 2 |
| C7×#808 | 2 |
| C7×#807 | 2 |
| C7×C4⋊(C3⋊C8) | 2 |
| C7×#478 | 3 |
| #5009 | 7 |