Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
186 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 35 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. D4×C22⋊ΓL(1,𝔽8) | C2 | semidirect |
| 2. C8×C22⋊ΓL(1,𝔽8) | C2 | semidirect |
| 3. C22×C7×D8 | C3 | semidirect |
| 7. C22×C7×D4 | C2×C3 | semidirect |
| 11. C22×C7×C8 | C2×C3 | semidirect |
| 25. C7×D8 | A4 | semidirect |
| 30. C22⋊ΓL(1,𝔽8) | D8 | direct (N × H) |
| 33. C22×D8 | ΓL(1,𝔽8) | semidirect |
| 42. C7×D4 | C2×A4 | semidirect |
| 46. C7×C8 | C2×A4 | semidirect |
| 52. C22×D4 | C2×ΓL(1,𝔽8) | semidirect |
| 56. C22×C8 | C2×ΓL(1,𝔽8) | semidirect |
| 65. C22×C7 | C3×D8 | semidirect |
| 81. D8 | C22⋊ΓL(1,𝔽8) | direct (N × H) |
| 100. D4 | C2×C22⋊ΓL(1,𝔽8) | semidirect |
| 104. C8 | C2×C22⋊ΓL(1,𝔽8) | semidirect |
| 105. C7 | A4×D8 | semidirect |
| 116. C22 | D8×ΓL(1,𝔽8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C22⋊ΓL(1,𝔽8) | 2 |
| C8×C22⋊ΓL(1,𝔽8) | 2 |
| C22×C7×D8 | 3 |
| D8×ΓL(1,𝔽8) | 4 |
| A4×D8 | 7 |