Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
588 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 211 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. C3×C4×C7×Q8 | C2 | semidirect |
| 3. Q8×Dic21 | C2 | semidirect |
| 4. #10621376 | C2 | semidirect |
| 5. C4⋊C4×D21 | C2 | semidirect |
| 6. C4×D84 | C2 | semidirect |
| 7. #10621355 | C2 | semidirect |
| 10. #66732 | C4 | semidirect |
| 23. C4×C7×Q8 | D3 | semidirect |
| 31. C3×C7×Q8 | C2×C4 | semidirect |
| 38. D84 | C2×C4 | semidirect |
| 40. C4×D21 | C2×C4 | semidirect |
| 55. C3×C4×Q8 | D7 | semidirect |
| 73. C7×Q8 | C4×D3 | semidirect |
| 102. C4×Q8 | D21 | semidirect |
| 118. C3×Q8 | C4×D7 | semidirect |
| 128. C3×C7 | #520 | semidirect |
| 157. Q8 | C4×D21 | semidirect |
| 167. C7 | #5574 | semidirect |
| 182. C3 | #90265 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66732 | 2 |
| C3×C4×C7×Q8 | 2 |
| Q8×Dic21 | 2 |
| #10621376 | 2 |
| C4⋊C4×D21 | 2 |
| C4×D84 | 2 |
| #10621355 | 2 |
| #90265 | 3 |
| #5574 | 7 |