Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
410 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 69 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. Q8×C22⋊ΓL(1,𝔽8) | C2 | semidirect |
| 3. Dic14⋊A4 | C2 | semidirect |
| 4. C22×Q8×D7 | C3 | semidirect |
| 9. C22×C7×Q8 | C2×C3 | semidirect |
| 15. C22×Dic14 | C2×C3 | semidirect |
| 18. D7⋊A4 | Q8 | direct (N × H) |
| 33. Q8×D7 | A4 | semidirect |
| 44. C22⋊ΓL(1,𝔽8) | C2×Q8 | semidirect |
| 53. C22×D7 | C3×Q8 | semidirect |
| 56. C7×Q8 | C2×A4 | semidirect |
| 69. Dic14 | C2×A4 | semidirect |
| 81. C22×Q8 | AGL(1,𝔽7) | semidirect |
| 85. C22×C7 | C2×C3×Q8 | semidirect |
| 125. D7 | Q8×A4 | semidirect |
| 141. Q8 | D7⋊A4 | direct (N × H) |
| 151. C7 | C2×Q8×A4 | semidirect |
| 162. C22 | Q8×AGL(1,𝔽7) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C22⋊ΓL(1,𝔽8) | 2 |
| C4×D7⋊A4 | 2 |
| Dic14⋊A4 | 2 |
| C22×Q8×D7 | 3 |
| Q8×AGL(1,𝔽7) | 4 |
| C2×Q8×A4 | 7 |