Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
304 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 78 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. C3×C7×#137 | C2 | semidirect |
| 3. C7×#947 | C2 | semidirect |
| 4. C7×#942 | C2 | semidirect |
| 5. C7×#837 | C2 | semidirect |
| 6. C7×#825 | C2 | semidirect |
| 7. C7×#823 | C2 | semidirect |
| 10. C2×C3×C7×Q8 | C22 | semidirect |
| 20. C3×C7×M16 | C22 | semidirect |
| 24. C4×C7×Dic3 | C22 | semidirect |
| 25. C7×#208 | C22 | semidirect |
| 28. C7×#137 | D3 | semidirect |
| 33. #5202 | C7 | direct (N × H) |
| 60. C2×C7×Q8 | C2×D3 | semidirect |
| 70. C7×M16 | C2×D3 | semidirect |
| 74. C3×#137 | C2×C7 | semidirect |
| 75. #947 | C2×C7 | semidirect |
| 76. #942 | C2×C7 | semidirect |
| 77. #837 | C2×C7 | semidirect |
| 78. #825 | C2×C7 | semidirect |
| 79. #823 | C2×C7 | semidirect |
| 116. C2×C3×Q8 | C22×C7 | semidirect |
| 126. C3×M16 | C22×C7 | semidirect |
| 130. C4×Dic3 | C22×C7 | semidirect |
| 131. #208 | C22×C7 | semidirect |
| 139. #137 | D3×C7 | semidirect |
| 178. C3×C7 | #455 | semidirect |
| 183. C2×Q8 | C2×D3×C7 | semidirect |
| 193. M16 | C2×D3×C7 | semidirect |
| 235. C7 | #5202 | direct (N × H) |
| 253. C3 | C7×#455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1009 | 2 |
| C3×C7×#137 | 2 |
| C7×#947 | 2 |
| C7×#942 | 2 |
| C7×#837 | 2 |
| C7×#825 | 2 |
| C7×#823 | 2 |
| C7×#455 | 3 |
| #5202 | 7 |