Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
620 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 204 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. C2×#1157⋊C3 | C2 | semidirect |
| 2. C2×C42×ΓL(1,𝔽8) | C2 | semidirect |
| 3. #6493⋊C3 | C2 | semidirect |
| 4. #6438⋊C3 | C2 | semidirect |
| 5. #10620710 | C2 | semidirect |
| 6. C4×C4⋊AGL(1,𝔽7) | C2 | semidirect |
| 7. #6432⋊C3 | C2 | semidirect |
| 8. #90168 | C3 | semidirect |
| 22. C2×#1157 | C2×C3 | semidirect |
| 23. C2×C42×C7 | C2×C3 | semidirect |
| 24. #6493 | C2×C3 | semidirect |
| 25. #6438 | C2×C3 | semidirect |
| 26. #6437 | C2×C3 | semidirect |
| 27. C4×D28 | C2×C3 | semidirect |
| 28. #6432 | C2×C3 | semidirect |
| 33. C2×C4×ΓL(1,𝔽8) | D4 | semidirect |
| 72. C4×ΓL(1,𝔽8) | #41 | semidirect |
| 78. C2×C4×C7 | C3×D4 | semidirect |
| 112. C2×C42 | AGL(1,𝔽7) | semidirect |
| 121. C4×C7 | C3×#41 | semidirect |
| 137. ΓL(1,𝔽8) | #532 | semidirect |
| 174. C2×C4 | C4⋊AGL(1,𝔽7) | semidirect |
| 179. C7 | C3×#532 | semidirect |
| 193. C4 | #1157⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1157⋊C3 | 2 |
| C2×C42×ΓL(1,𝔽8) | 2 |
| #6493⋊C3 | 2 |
| #6438⋊C3 | 2 |
| #10620710 | 2 |
| C4×C4⋊AGL(1,𝔽7) | 2 |
| #6432⋊C3 | 2 |
| #90168 | 3 |
| C3×#532 | 7 |