Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 180 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 |
|---|---|---|
| 8. #89794 | C3 | semidirect |
| 119. ΓL(1,𝔽8) | #479 | semidirect |
| 154. C7 | C3×#479 | 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 |
| #6433⋊C3 | 2 |
| #6409⋊C3 | 2 |
| #6382⋊C3 | 2 |
| #6381⋊C3 | 2 |
| C4⋊(ΓL(1,𝔽8)⋊C8) | 2 |
| #89794 | 3 |
| C3×#479 | 7 |