Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 70 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×#932 | C2 | semidirect |
| 2. C2×C7×#213 | C2 | semidirect |
| 3. C7×#908 | C2 | semidirect |
| 4. C7×#907 | C2 | semidirect |
| 5. C3×C7×#100 | C2 | semidirect |
| 6. C7×#823 | C2 | semidirect |
| 7. C7×#822 | C2 | semidirect |
| 30. C7×#100 | D3 | semidirect |
| 31. #4749 | C7 | direct (N × H) |
| 63. #932 | C2×C7 | semidirect |
| 64. C2×#213 | C2×C7 | semidirect |
| 65. #908 | C2×C7 | semidirect |
| 66. #907 | C2×C7 | semidirect |
| 67. C3×#100 | C2×C7 | semidirect |
| 68. #823 | C2×C7 | semidirect |
| 69. #822 | C2×C7 | semidirect |
| 122. #100 | D3×C7 | semidirect |
| 148. C3×C7 | #472 | semidirect |
| 194. C7 | #4749 | direct (N × H) |
| 209. C3 | C7×#472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#932 | 2 |
| C2×C7×#213 | 2 |
| C7×#908 | 2 |
| C7×#907 | 2 |
| C3×C7×#100 | 2 |
| C7×#823 | 2 |
| C7×#822 | 2 |
| C7×#472 | 3 |
| #4749 | 7 |