Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 70 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. #6451⋊C3 | C2 | semidirect |
| 3. ΓL(1,𝔽8)×#106 | C2 | semidirect |
| 5. (ΓL(1,𝔽8)⋊C4)⋊C8 | C2 | semidirect |
| 7. #6382⋊C3 | C2 | semidirect |
| 8. #89642 | C3 | semidirect |
| 21. #6451 | C2×C3 | semidirect |
| 22. C7×#106 | C2×C3 | semidirect |
| 24. Dic7⋊C8 | C2×C3 | semidirect |
| 26. #6382 | C2×C3 | semidirect |
| 36. C4⋊AGL(1,𝔽7) | Q8 | semidirect |
| 79. D28 | C3×Q8 | semidirect |
| 102. #106 | AGL(1,𝔽7) | semidirect |
| 130. ΓL(1,𝔽8) | #476 | semidirect |
| 170. C7 | C3×#476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6456⋊C3 | 2 |
| #6451⋊C3 | 2 |
| ΓL(1,𝔽8)×#106 | 2 |
| #6395⋊C3 | 2 |
| (ΓL(1,𝔽8)⋊C4)⋊C8 | 2 |
| #6383⋊C3 | 2 |
| #6382⋊C3 | 2 |
| #89642 | 3 |
| C3×#476 | 7 |