Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
300 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 300 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 |
|---|---|---|
| 2. M16×D21 | C2 | semidirect |
| 3. #10620854 | C2 | semidirect |
| 4. C7×#823 | C2 | semidirect |
| 5. C3×#6398 | C2 | semidirect |
| 6. #10620496 | C2 | semidirect |
| 7. #10620494 | C2 | semidirect |
| 32. #6398 | D3 | semidirect |
| 78. #823 | D7 | semidirect |
| 173. C3×C7 | #413 | semidirect |
| 228. C7 | #4751 | semidirect |
| 245. C3 | #89517 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66672 | 2 |
| M16×D21 | 2 |
| #10620854 | 2 |
| C7×#823 | 2 |
| C3×#6398 | 2 |
| #10620496 | 2 |
| #10620494 | 2 |
| #89517 | 3 |
| #4751 | 7 |