Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
188 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 111 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. C7×#446 | C3 | semidirect |
| 29. C8×ΓL(1,𝔽8) | Q8 | semidirect |
| 50. #446 | ΓL(1,𝔽8) | direct (N × H) |
| 59. C7×C8 | C3×Q8 | semidirect |
| 92. ΓL(1,𝔽8) | #446 | direct (N × H) |
| 119. C8 | Q8×ΓL(1,𝔽8) | semidirect |
| 120. C7 | C3×#446 | 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 |
| ΓL(1,𝔽8)×C4⋊C8 | 2 |
| ΓL(1,𝔽8)×#97 | 2 |
| C4×C8×ΓL(1,𝔽8) | 2 |
| C7×#446 | 3 |
| C3×#446 | 7 |