Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 76 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. C22×C8×ΓL(1,𝔽8) | C2 | semidirect |
| 2. #6493⋊C3 | C2 | semidirect |
| 3. C2×D56⋊C3 | C2 | semidirect |
| 4. #6395⋊C3 | C2 | semidirect |
| 5. #6392⋊C3 | C2 | semidirect |
| 6. #89887 | C3 | semidirect |
| 16. C22×C7×C8 | C2×C3 | semidirect |
| 17. #6493 | C2×C3 | semidirect |
| 18. C2×D56 | C2×C3 | semidirect |
| 19. #6395 | C2×C3 | semidirect |
| 20. #6392 | C2×C3 | semidirect |
| 33. C8×ΓL(1,𝔽8) | D4 | semidirect |
| 50. C22×ΓL(1,𝔽8) | D8 | semidirect |
| 71. C7×C8 | C3×D4 | semidirect |
| 87. C22×C8 | AGL(1,𝔽7) | semidirect |
| 93. C22×C7 | C3×D8 | semidirect |
| 114. ΓL(1,𝔽8) | #466 | semidirect |
| 151. C8 | (C22⋊D7)⋊C3 | semidirect |
| 152. C7 | C3×#466 | semidirect |
| 163. C22 | D56⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×ΓL(1,𝔽8) | 2 |
| #6493⋊C3 | 2 |
| C2×D56⋊C3 | 2 |
| #6395⋊C3 | 2 |
| #6392⋊C3 | 2 |
| #89887 | 3 |
| C3×#466 | 7 |