Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 98 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. ΓL(1,𝔽8)×#117 | C2 | semidirect |
| 3. #6489⋊C3 | C2 | semidirect |
| 4. #6380⋊C3 | C2 | semidirect |
| 5. #89778 | C3 | semidirect |
| 12. C2×C4⋊AGL(1,𝔽7) | C4 | semidirect |
| 13. C2×C4×AGL(1,𝔽7) | C4 | semidirect |
| 14. C2×ΓL(1,𝔽8)⋊Q8 | C4 | semidirect |
| 22. C7×#117 | C2×C3 | semidirect |
| 23. #6489 | C2×C3 | semidirect |
| 24. #6380 | C2×C3 | semidirect |
| 51. C2×D28 | C3×C4 | semidirect |
| 52. C2×C4×D7 | C3×C4 | semidirect |
| 53. C2×Dic14 | C3×C4 | semidirect |
| 119. #117 | AGL(1,𝔽7) | semidirect |
| 153. ΓL(1,𝔽8) | #410 | semidirect |
| 206. C7 | C3×#410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1157⋊C3 | 2 |
| ΓL(1,𝔽8)×#117 | 2 |
| #6489⋊C3 | 2 |
| #6380⋊C3 | 2 |
| #89778 | 3 |
| C3×#410 | 7 |