Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
292 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 4. C7×#824 | C2 | semidirect |
| 5. C3×#6398 | C2 | semidirect |
| 6. #10620497 | C2 | semidirect |
| 7. #10620496 | C2 | semidirect |
| 32. #6398 | D3 | semidirect |
| 78. #824 | D7 | semidirect |
| 131. D21 | #101 | semidirect |
| 170. C3×C7 | C2×#101 | semidirect |
| 223. C7 | D3×#101 | semidirect |
| 238. C3 | D7×#101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D21⋊Q8 | 2 |
| M16×D21 | 2 |
| #10620854 | 2 |
| C7×#824 | 2 |
| C3×#6398 | 2 |
| #10620497 | 2 |
| #10620496 | 2 |
| D7×#101 | 3 |
| D3×#101 | 7 |