Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 6. #89792 | C3 | semidirect |
| 23. Q8×ΓL(1,𝔽8) | Q8 | semidirect |
| 56. C7×Q8 | C3×Q8 | semidirect |
| 100. ΓL(1,𝔽8) | #475 | semidirect |
| 123. Q8 | ΓL(1,𝔽8)⋊Q8 | semidirect |
| 131. C7 | C3×#475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×ΓL(1,𝔽8) | 2 |
| #6432⋊C3 | 2 |
| #6409⋊C3 | 2 |
| #6382⋊C3 | 2 |
| C4⋊(ΓL(1,𝔽8)⋊C8) | 2 |
| #89792 | 3 |
| C3×#475 | 7 |