Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 104 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. C2×M16×ΓL(1,𝔽8) | C2 | semidirect |
| 3. C2×C4⋊(ΓL(1,𝔽8)⋊C4) | C2 | semidirect |
| 4. #6395⋊C3 | C2 | semidirect |
| 5. #6390⋊C3 | C2 | semidirect |
| 6. #89905 | C3 | semidirect |
| 11. #1157⋊C3 | C4 | semidirect |
| 20. C2×C7×M16 | C2×C3 | semidirect |
| 21. C2×C4⋊Dic7 | C2×C3 | semidirect |
| 22. #6395 | C2×C3 | semidirect |
| 23. #6390 | C2×C3 | semidirect |
| 36. C4⋊AGL(1,𝔽7) | C2×C4 | semidirect |
| 39. ΓL(1,𝔽8)⋊Q8 | C2×C4 | semidirect |
| 45. #1157 | C3×C4 | semidirect |
| 82. D28 | C2×C3×C4 | semidirect |
| 85. Dic14 | C2×C3×C4 | semidirect |
| 105. C2×M16 | AGL(1,𝔽7) | semidirect |
| 137. ΓL(1,𝔽8) | #417 | semidirect |
| 183. C7 | C3×#417 | 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×M16×ΓL(1,𝔽8) | 2 |
| C2×C4⋊(ΓL(1,𝔽8)⋊C4) | 2 |
| #6395⋊C3 | 2 |
| #6390⋊C3 | 2 |
| #89905 | 3 |
| C3×#417 | 7 |