Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
212 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 90 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×#948 | C2 | semidirect |
| 3. C7×#907 | C2 | semidirect |
| 4. C3×C7×#104 | C2 | semidirect |
| 5. C7×#822 | C2 | semidirect |
| 6. C7×#805 | C2 | semidirect |
| 7. C4×C7×C3⋊C8 | C2 | semidirect |
| 13. C7×#216 | C4 | semidirect |
| 14. C7×#215 | C4 | semidirect |
| 15. C7×#214 | C4 | semidirect |
| 16. C7×#213 | C4 | semidirect |
| 29. C7×#104 | D3 | semidirect |
| 31. #4824 | C7 | direct (N × H) |
| 64. #948 | C2×C7 | semidirect |
| 65. #907 | C2×C7 | semidirect |
| 66. C3×#104 | C2×C7 | semidirect |
| 67. #822 | C2×C7 | semidirect |
| 68. #805 | C2×C7 | semidirect |
| 69. C4×C3⋊C8 | C2×C7 | semidirect |
| 99. #216 | C4×C7 | semidirect |
| 100. #215 | C4×C7 | semidirect |
| 101. #214 | C4×C7 | semidirect |
| 102. #213 | C4×C7 | semidirect |
| 119. #104 | D3×C7 | semidirect |
| 145. C3×C7 | #443 | semidirect |
| 189. C7 | #4824 | direct (N × H) |
| 202. C3 | C7×#443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#950 | 2 |
| C7×#948 | 2 |
| C7×#907 | 2 |
| C3×C7×#104 | 2 |
| C7×#822 | 2 |
| C7×#805 | 2 |
| C4×C7×C3⋊C8 | 2 |
| C7×#443 | 3 |
| #4824 | 7 |