Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
660 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 288 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 |
|---|---|---|
| 3. ΓL(1,𝔽8)⋊#95 | C2 | direct (N × H) |
| 4. C2×C7⋊#95 | C3 | semidirect |
| 7. C22×C4×ΓL(1,𝔽8) | C4 | semidirect |
| 11. C22×ΓL(1,𝔽8)⋊C4 | C4 | semidirect |
| 15. C7⋊#95 | C2×C3 | semidirect |
| 25. C2×C4×ΓL(1,𝔽8) | C2×C4 | semidirect |
| 29. C2×ΓL(1,𝔽8)⋊C4 | C2×C4 | semidirect |
| 32. C22×C4×C7 | C3×C4 | semidirect |
| 36. C22×Dic7 | C3×C4 | semidirect |
| 62. C2×C4×C7 | C2×C3×C4 | semidirect |
| 66. C2×Dic7 | C2×C3×C4 | semidirect |
| 75. C2×ΓL(1,𝔽8) | #95 | semidirect |
| 109. ΓL(1,𝔽8) | C2×#95 | semidirect |
| 116. C22×C4 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 118. C2×C7 | C3×#95 | semidirect |
| 148. C2×C4 | C2×ΓL(1,𝔽8)⋊C4 | semidirect |
| 149. C7 | C2×C3×#95 | semidirect |
| 169. C2 | ΓL(1,𝔽8)⋊#95 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×ΓL(1,𝔽8) | 2 |
| C23×ΓL(1,𝔽8)⋊C4 | 2 |
| ΓL(1,𝔽8)⋊#95 | 2 |
| C2×C7⋊#95 | 3 |
| C2×C3×#95 | 7 |