Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
284 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 284 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×#944 | C2 | semidirect |
| 4. C7×#942 | C2 | semidirect |
| 5. C7×#837 | C2 | semidirect |
| 6. C7×#825 | C2 | semidirect |
| 7. C7×#824 | C2 | semidirect |
| 28. C7×#137 | D3 | semidirect |
| 33. #5205 | C7 | direct (N × H) |
| 74. C3×#137 | C2×C7 | semidirect |
| 75. #944 | C2×C7 | semidirect |
| 76. #942 | C2×C7 | semidirect |
| 77. #837 | C2×C7 | semidirect |
| 78. #825 | C2×C7 | semidirect |
| 79. #824 | C2×C7 | semidirect |
| 136. #137 | D3×C7 | semidirect |
| 173. C3×C7 | #456 | semidirect |
| 227. C7 | #5205 | direct (N × H) |
| 242. C3 | C7×#456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1010 | 2 |
| C3×C7×#137 | 2 |
| C7×#944 | 2 |
| C7×#942 | 2 |
| C7×#837 | 2 |
| C7×#825 | 2 |
| C7×#824 | 2 |
| C7×#456 | 3 |
| #5205 | 7 |