Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
372 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 2. C2×C4⋊(ΓL(1,𝔽8)⋊C4) | C2 | semidirect |
| 3. ΓL(1,𝔽8)×#95 | C2 | semidirect |
| 4. #89449 | C3 | semidirect |
| 11. C2×C4⋊Dic7 | C2×C3 | semidirect |
| 12. C7×#95 | C2×C3 | semidirect |
| 58. #95 | AGL(1,𝔽7) | semidirect |
| 75. ΓL(1,𝔽8) | #399 | semidirect |
| 101. C7 | C3×#399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C2×AGL(1,𝔽7))⋊C4 | 2 |
| C2×C4⋊(ΓL(1,𝔽8)⋊C4) | 2 |
| ΓL(1,𝔽8)×#95 | 2 |
| #89449 | 3 |
| C3×#399 | 7 |