Finite Group DatabasebetaFinite Group Databasebeta← C2×(C2×AGL(1,𝔽7))⋊C8 #13052007
Order 1344.
404 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 144 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. C22×C8×ΓL(1,𝔽8) | C2 | semidirect |
| 3. C22×ΓL(1,𝔽8)⋊C8 | C2 | semidirect |
| 4. (C2×AGL(1,𝔽7))⋊C8 | C2 | direct (N × H) |
| 5. C2×(C2×D7)⋊C8 | C3 | semidirect |
| 14. C2×C8×ΓL(1,𝔽8) | C22 | semidirect |
| 16. C2×ΓL(1,𝔽8)⋊C8 | C22 | semidirect |
| 18. C22×C7×C8 | C2×C3 | semidirect |
| 19. C22×C7⋊C8 | C2×C3 | semidirect |
| 20. (C2×D7)⋊C8 | C2×C3 | semidirect |
| 25. C22×AGL(1,𝔽7) | C8 | semidirect |
| 46. C2×C7×C8 | C22×C3 | semidirect |
| 48. C2×C7⋊C8 | C22×C3 | semidirect |
| 60. C2×AGL(1,𝔽7) | C2×C8 | semidirect |
| 69. C22×D7 | C3×C8 | semidirect |
| 93. C2×ΓL(1,𝔽8) | C22⋊C8 | semidirect |
| 100. C22×C8 | AGL(1,𝔽7) | semidirect |
| 109. C2×D7 | C2×C3×C8 | semidirect |
| 130. ΓL(1,𝔽8) | C2×C22⋊C8 | semidirect |
| 141. C2×C8 | C2×AGL(1,𝔽7) | semidirect |
| 142. C2×C7 | C3×C22⋊C8 | semidirect |
| 175. C7 | C2×C3×C22⋊C8 | semidirect |
| 195. C2 | (C2×AGL(1,𝔽7))⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×AGL(1,𝔽7) | 2 |
| C22×C8×ΓL(1,𝔽8) | 2 |
| C22×ΓL(1,𝔽8)⋊C8 | 2 |
| (C2×AGL(1,𝔽7))⋊C8 | 2 |
| C2×(C2×D7)⋊C8 | 3 |
| C2×C3×C22⋊C8 | 7 |