Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
404 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 404 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 |
|---|---|---|
| 1. C22×Q8×ΓL(1,𝔽8) | C2 | semidirect |
| 3. ΓL(1,𝔽8)⋊#95 | C2 | semidirect |
| 4. #90003 | C3 | semidirect |
| 10. C22×C7×Q8 | C2×C3 | semidirect |
| 12. C7⋊#95 | C2×C3 | semidirect |
| 17. C22×AGL(1,𝔽7) | Q8 | semidirect |
| 43. C22×D7 | C3×Q8 | semidirect |
| 58. C22×Q8 | AGL(1,𝔽7) | semidirect |
| 78. ΓL(1,𝔽8) | #393 | semidirect |
| 105. C7 | C3×#393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×ΓL(1,𝔽8) | 2 |
| C2×(C2×AGL(1,𝔽7))⋊C4 | 2 |
| ΓL(1,𝔽8)⋊#95 | 2 |
| #90003 | 3 |
| C3×#393 | 7 |