Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
280 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 280 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. C4×D4×ΓL(1,𝔽8) | C2 | semidirect |
| 2. C2×#1141⋊C3 | C2 | semidirect |
| 3. #10620710 | C2 | semidirect |
| 4. #6383⋊C3 | C2 | semidirect |
| 5. C4⋊(ΓL(1,𝔽8)⋊C8) | C2 | semidirect |
| 6. #89787 | C3 | semidirect |
| 17. C4×C7×D4 | C2×C3 | semidirect |
| 18. C2×#1141 | C2×C3 | semidirect |
| 19. #6437 | C2×C3 | semidirect |
| 20. #6383 | C2×C3 | semidirect |
| 21. C4⋊(C7⋊C8) | C2×C3 | semidirect |
| 26. D4×ΓL(1,𝔽8) | D4 | semidirect |
| 61. C4×ΓL(1,𝔽8) | D8 | semidirect |
| 68. C7×D4 | C3×D4 | semidirect |
| 96. C4×D4 | AGL(1,𝔽7) | semidirect |
| 108. C4×C7 | C3×D8 | semidirect |
| 125. ΓL(1,𝔽8) | #459 | semidirect |
| 160. D4 | C4⋊AGL(1,𝔽7) | semidirect |
| 167. C7 | C3×#459 | semidirect |
| 182. C4 | #1141⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×ΓL(1,𝔽8) | 2 |
| C2×#1141⋊C3 | 2 |
| #10620710 | 2 |
| #6383⋊C3 | 2 |
| C4⋊(ΓL(1,𝔽8)⋊C8) | 2 |
| #89787 | 3 |
| C3×#459 | 7 |