Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 1. C3×C4×C7×Q8 | C2 | semidirect |
| 4. C3×#6409 | C2 | semidirect |
| 6. C3×#6381 | C2 | semidirect |
| 7. C3×#6377 | C2 | semidirect |
| 8. #89798 | C3 | direct (N × H) |
| 16. C3×#1143 | C4 | semidirect |
| 21. C4×C7×Q8 | C2×C3 | semidirect |
| 24. #6409 | C2×C3 | semidirect |
| 26. #6381 | C2×C3 | semidirect |
| 27. #6377 | C2×C3 | semidirect |
| 31. C3×C7×Q8 | C2×C4 | semidirect |
| 42. C3×C7⋊C8 | C2×C4 | semidirect |
| 50. #1143 | C3×C4 | semidirect |
| 56. C3×C4×Q8 | D7 | semidirect |
| 76. C7×Q8 | C2×C3×C4 | semidirect |
| 87. C7⋊C8 | C2×C3×C4 | semidirect |
| 105. C4×Q8 | C3×D7 | semidirect |
| 124. C3×Q8 | C4×D7 | semidirect |
| 136. C3×C7 | #440 | semidirect |
| 166. Q8 | C3×C4×D7 | semidirect |
| 178. C7 | C3×#440 | semidirect |
| 194. C3 | #89798 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×Q8 | 2 |
| C2×C3×#1143 | 2 |
| C3×C4×D28 | 2 |
| C3×#6409 | 2 |
| C3×#6383 | 2 |
| C3×#6381 | 2 |
| C3×#6377 | 2 |
| #89798 | 3 |
| C3×#440 | 7 |