Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
220 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 220 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. C2×C7×#216 | C2 | semidirect |
| 5. C3×C7×#103 | C2 | semidirect |
| 6. C7×#816 | C2 | semidirect |
| 7. C7×#808 | C2 | semidirect |
| 28. C7×#103 | D3 | semidirect |
| 29. #4816 | C7 | direct (N × H) |
| 59. C2×#216 | C2×C7 | semidirect |
| 62. C3×#103 | C2×C7 | semidirect |
| 63. #816 | C2×C7 | semidirect |
| 64. #808 | C2×C7 | semidirect |
| 115. #103 | D3×C7 | semidirect |
| 142. C3×C7 | #470 | semidirect |
| 186. C7 | #4816 | direct (N × H) |
| 202. C3 | C7×#470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#946 | 2 |
| C2×C7×#216 | 2 |
| C2×C7×ΓL(1,𝔽25) | 2 |
| C7×#897 | 2 |
| C3×C7×#103 | 2 |
| C7×#816 | 2 |
| C7×#808 | 2 |
| C7×#470 | 3 |
| #4816 | 7 |