Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
292 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 292 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 |
|---|---|---|
| 1. C7×#1010 | C2 | semidirect |
| 2. C7×#949 | C2 | semidirect |
| 3. C7×#908 | C2 | semidirect |
| 4. C7×#875 | C2 | semidirect |
| 5. C3×C7×#104 | C2 | semidirect |
| 6. C7×#824 | C2 | semidirect |
| 7. C7×#805 | C2 | semidirect |
| 31. C7×#104 | D3 | semidirect |
| 33. #4827 | C7 | direct (N × H) |
| 73. #1010 | C2×C7 | semidirect |
| 74. #949 | C2×C7 | semidirect |
| 75. #908 | C2×C7 | semidirect |
| 76. #875 | C2×C7 | semidirect |
| 77. C3×#104 | C2×C7 | semidirect |
| 78. #824 | C2×C7 | semidirect |
| 79. #805 | C2×C7 | semidirect |
| 141. #104 | D3×C7 | semidirect |
| 176. C3×C7 | #454 | semidirect |
| 232. C7 | #4827 | direct (N × H) |
| 249. C3 | C7×#454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1010 | 2 |
| C7×#949 | 2 |
| C7×#908 | 2 |
| C7×#875 | 2 |
| C3×C7×#104 | 2 |
| C7×#824 | 2 |
| C7×#805 | 2 |
| C7×#454 | 3 |
| #4827 | 7 |