Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
634 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 73 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×D7⋊A4 | C2 | semidirect |
| 2. C2×C4×C22⋊ΓL(1,𝔽8) | C2 | semidirect |
| 3. C4⋊(D7⋊A4) | C2 | direct (N × H) |
| 4. C23×D28 | C3 | semidirect |
| 7. C2×D7⋊A4 | C22 | semidirect |
| 8. C4×C22⋊ΓL(1,𝔽8) | C22 | semidirect |
| 10. C24×D7 | C2×C3 | semidirect |
| 11. C23×C4×C7 | C2×C3 | semidirect |
| 16. C22×D28 | C2×C3 | semidirect |
| 18. C2×C22⋊ΓL(1,𝔽8) | D4 | semidirect |
| 30. C23×D7 | C22×C3 | semidirect |
| 34. C22×C4×C7 | C22×C3 | semidirect |
| 44. C2×D28 | A4 | semidirect |
| 48. C22⋊ΓL(1,𝔽8) | C2×D4 | semidirect |
| 57. C23×C7 | C3×D4 | semidirect |
| 72. C22×D7 | C2×A4 | semidirect |
| 78. C2×C4×C7 | C2×A4 | semidirect |
| 82. D28 | C2×A4 | semidirect |
| 97. C23×C4 | AGL(1,𝔽7) | semidirect |
| 105. C22×C7 | C2×C3×D4 | semidirect |
| 116. C2×D7 | C22×A4 | semidirect |
| 118. C4×C7 | C22×A4 | semidirect |
| 146. C22×C4 | C2×AGL(1,𝔽7) | semidirect |
| 150. C2×C7 | D4×A4 | semidirect |
| 176. C23 | C4⋊AGL(1,𝔽7) | semidirect |
| 187. C2×C4 | D7⋊A4 | semidirect |
| 188. C7 | C2×D4×A4 | semidirect |
| 209. C22 | C2×C4⋊AGL(1,𝔽7) | semidirect |
| 212. C4 | C2×D7⋊A4 | semidirect |
| 219. C2 | C4⋊(D7⋊A4) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D7⋊A4 | 2 |
| C2×C4×C22⋊ΓL(1,𝔽8) | 2 |
| C4⋊(D7⋊A4) | 2 |
| C23×D28 | 3 |
| C2×C4⋊AGL(1,𝔽7) | 4 |
| C2×D4×A4 | 7 |