Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 64 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. #6409⋊C3 | C2 | semidirect |
| 4. #6409⋊C3 | C2 | semidirect |
| 6. #6382⋊C3 | C2 | semidirect |
| 7. #6381⋊C3 | C2 | semidirect |
| 8. #89817 | C3 | semidirect |
| 22. #6409 | C2×C3 | semidirect |
| 23. #6409 | C2×C3 | semidirect |
| 25. #6382 | C2×C3 | semidirect |
| 26. #6381 | C2×C3 | semidirect |
| 130. ΓL(1,𝔽8) | #485 | semidirect |
| 170. C7 | C3×#485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×C22⋊Q8 | 2 |
| #6489⋊C3 | 2 |
| #6409⋊C3 | 2 |
| (C22⋊(C7⋊C8))⋊C3 | 2 |
| #6382⋊C3 | 2 |
| #6381⋊C3 | 2 |
| #89817 | 3 |
| C3×#485 | 7 |