Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
164 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 164 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. #6403⋊C3 | C2 | direct (N × H) |
| 5. C2×#6403 | C3 | semidirect |
| 16. #6403 | C2×C3 | semidirect |
| 63. C2×ΓL(1,𝔽8) | Q32 | semidirect |
| 83. ΓL(1,𝔽8) | C2×Q32 | semidirect |
| 92. C2×C7 | C3×Q32 | semidirect |
| 108. C7 | C2×C3×Q32 | semidirect |
| 117. C2 | #6403⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×ΓL(1,𝔽8) | 2 |
| C2×Dic28⋊C3 | 2 |
| #6403⋊C3 | 2 |
| C2×ΓL(1,𝔽8)⋊C16 | 2 |
| C2×#6403 | 3 |
| C2×C3×Q32 | 7 |