Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 324 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 |
|---|---|---|
| 4. #10620649 | C2 | semidirect |
| 5. C7×#810 | C2 | semidirect |
| 6. #10620509 | C2 | semidirect |
| 7. #10620507 | C2 | semidirect |
| 16. D7×Dic6 | C4 | semidirect |
| 36. Dic42 | C2×C4 | semidirect |
| 39. C7×Dic6 | C2×C4 | semidirect |
| 69. #810 | D7 | direct (N × H) |
| 117. C3×D7 | #103 | semidirect |
| 151. Dic6 | C4×D7 | semidirect |
| 154. C3×C7 | C2×#103 | semidirect |
| 172. D7 | #810 | direct (N × H) |
| 202. C7 | C2×#810 | semidirect |
| 218. C3 | D7×#103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×Dic6 | 2 |
| C3×D7×C4⋊C4 | 2 |
| C2×D7×C3⋊C8 | 2 |
| #10620649 | 2 |
| C7×#810 | 2 |
| #10620509 | 2 |
| #10620507 | 2 |
| D7×#103 | 3 |
| C2×#810 | 7 |