Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
260 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 260 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 |
|---|---|---|
| 1. C2×C3×C7×M16 | C2 | semidirect |
| 2. C7×#930 | C2 | semidirect |
| 3. C2×C7×D24 | C2 | semidirect |
| 4. C7×#821 | C2 | semidirect |
| 5. C7×#817 | C2 | semidirect |
| 17. C2×C7×M16 | D3 | semidirect |
| 21. #5135 | C7 | direct (N × H) |
| 33. C3×C7×C8 | D4 | semidirect |
| 43. C2×C3×M16 | C2×C7 | semidirect |
| 44. #930 | C2×C7 | semidirect |
| 45. C2×D24 | C2×C7 | semidirect |
| 46. #821 | C2×C7 | semidirect |
| 47. #817 | C2×C7 | semidirect |
| 70. C7×C8 | #67 | semidirect |
| 85. C2×M16 | D3×C7 | semidirect |
| 110. C3×C8 | C7×D4 | semidirect |
| 111. C3×C7 | #469 | semidirect |
| 146. C8 | C7×#67 | semidirect |
| 147. C7 | #5135 | direct (N × H) |
| 162. C3 | C7×#469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×M16 | 2 |
| C7×#930 | 2 |
| C2×C7×D24 | 2 |
| C7×#821 | 2 |
| C7×#817 | 2 |
| C7×#469 | 3 |
| #5135 | 7 |