Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
292 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 92 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. #10620675 | C2 | semidirect |
| 4. C3×#6410 | C2 | semidirect |
| 5. #10620497 | C2 | semidirect |
| 22. #6410 | D3 | direct (N × H) |
| 91. D3×C7 | #101 | semidirect |
| 119. C3×C7 | C2×#101 | semidirect |
| 157. C7 | D3×#101 | semidirect |
| 161. D3 | #6410 | direct (N × H) |
| 170. C3 | C2×#6410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C7×Q8 | 2 |
| D3×#1136 | 2 |
| #10620675 | 2 |
| C3×#6410 | 2 |
| #10620497 | 2 |
| C2×#6410 | 3 |
| D3×#101 | 7 |