Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
292 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 119 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. C3×C7×#97 | C2 | semidirect |
| 4. #10620654 | C2 | semidirect |
| 5. #10620642 | C2 | semidirect |
| 14. C8×D21 | C4 | semidirect |
| 17. C7×#97 | D3 | semidirect |
| 28. C3×C7×C8 | C2×C4 | semidirect |
| 29. C3⋊(C7⋊C8) | C2×C4 | semidirect |
| 40. C3×#97 | D7 | semidirect |
| 58. C7×C8 | C4×D3 | semidirect |
| 70. D21 | #97 | direct (N × H) |
| 75. #97 | D21 | direct (N × H) |
| 90. C3×C8 | C4×D7 | semidirect |
| 92. C3×C7 | C2×#97 | semidirect |
| 119. C8 | C4×D21 | semidirect |
| 120. C7 | D3×#97 | semidirect |
| 131. C3 | D7×#97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D21 | 2 |
| C42×D21 | 2 |
| C3×C7×#97 | 2 |
| #10620654 | 2 |
| #10620642 | 2 |
| D7×#97 | 3 |
| D3×#97 | 7 |