Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
252 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 252 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 |
|---|---|---|
| 4. #10620653 | C2 | semidirect |
| 5. C3×Dic7⋊C8 | C2 | semidirect |
| 6. #10620518 | C2 | semidirect |
| 7. Dic7⋊(C3⋊C8) | C2 | semidirect |
| 28. Dic7⋊C8 | D3 | semidirect |
| 72. Dic21 | M16 | semidirect |
| 74. C3×Dic7 | M16 | semidirect |
| 126. Dic7 | ΓL(1,𝔽25) | semidirect |
| 142. C3×C7 | #423 | semidirect |
| 186. C7 | #4837 | semidirect |
| 202. C3 | #89890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×ΓL(1,𝔽25) | 2 |
| C4×D3×Dic7 | 2 |
| C2×#66558 | 2 |
| #10620653 | 2 |
| C3×Dic7⋊C8 | 2 |
| #10620518 | 2 |
| Dic7⋊(C3⋊C8) | 2 |
| #89890 | 3 |
| #4837 | 7 |