Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 240 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×#946 | C2 | semidirect |
| 2. C2×C7×#215 | C2 | semidirect |
| 3. C2×C7×ΓL(1,𝔽25) | C2 | semidirect |
| 5. C3×C7×#103 | C2 | semidirect |
| 6. C7×#821 | C2 | semidirect |
| 7. C7×#807 | C2 | semidirect |
| 27. C7×#103 | D3 | semidirect |
| 29. #4812 | C7 | direct (N × H) |
| 45. C7×C3⋊C8 | D4 | semidirect |
| 59. #946 | C2×C7 | semidirect |
| 60. C2×#215 | C2×C7 | semidirect |
| 61. C2×ΓL(1,𝔽25) | C2×C7 | semidirect |
| 63. C3×#103 | C2×C7 | semidirect |
| 64. #821 | C2×C7 | semidirect |
| 65. #807 | C2×C7 | semidirect |
| 119. #103 | D3×C7 | semidirect |
| 149. C3⋊C8 | C7×D4 | semidirect |
| 150. C3×C7 | #468 | semidirect |
| 198. C7 | #4812 | direct (N × H) |
| 217. C3 | C7×#468 | 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×#215 | 2 |
| C2×C7×ΓL(1,𝔽25) | 2 |
| C7×#895 | 2 |
| C3×C7×#103 | 2 |
| C7×#821 | 2 |
| C7×#807 | 2 |
| C7×#468 | 3 |
| #4812 | 7 |