Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
200 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 200 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. C2×C7×#216 | C2 | semidirect |
| 5. C3×C7×#101 | C2 | semidirect |
| 6. C7×#824 | C2 | semidirect |
| 7. C7×#822 | C2 | semidirect |
| 30. C7×#101 | D3 | semidirect |
| 31. #4755 | C7 | direct (N × H) |
| 63. C2×#216 | C2×C7 | semidirect |
| 67. C3×#101 | C2×C7 | semidirect |
| 68. #824 | C2×C7 | semidirect |
| 69. #822 | C2×C7 | semidirect |
| 118. #101 | D3×C7 | semidirect |
| 142. C3×C7 | #473 | semidirect |
| 184. C7 | #4755 | direct (N × H) |
| 195. C3 | C7×#473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#216 | 2 |
| C7×#942 | 2 |
| C7×#909 | 2 |
| C7×#907 | 2 |
| C3×C7×#101 | 2 |
| C7×#824 | 2 |
| C7×#822 | 2 |
| C7×#473 | 3 |
| #4755 | 7 |