Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
492 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×C3×C7×C4⋊C4 | C2 | semidirect |
| 5. C2×C4⋊Dic21 | C2 | semidirect |
| 6. C2×#66629 | C2 | semidirect |
| 7. C2×C4×Dic21 | C2 | semidirect |
| 8. #10621381 | C2 | direct (N × H) |
| 17. C3×C7×C4⋊C4 | C22 | semidirect |
| 21. C4⋊Dic21 | C22 | semidirect |
| 22. #66629 | C22 | semidirect |
| 23. C4×Dic21 | C22 | semidirect |
| 24. C2×C7×C4⋊C4 | D3 | semidirect |
| 57. C7×C4⋊C4 | C2×D3 | semidirect |
| 64. C2×C3×C4⋊C4 | D7 | semidirect |
| 111. C3×C4⋊C4 | C2×D7 | semidirect |
| 118. C2×C3×C7 | #126 | semidirect |
| 126. C2×C4⋊C4 | D21 | semidirect |
| 162. C3×C7 | C2×#126 | semidirect |
| 172. C4⋊C4 | C2×D21 | semidirect |
| 177. C2×C7 | #898 | semidirect |
| 213. C7 | C2×#898 | semidirect |
| 214. C2×C3 | #6461 | semidirect |
| 233. C3 | C2×#6461 | semidirect |
| 235. C2 | #10621381 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×C4⋊C4 | 2 |
| C2×#66631 | 2 |
| C2×C4⋊Dic21 | 2 |
| C2×#66629 | 2 |
| C2×C4×Dic21 | 2 |
| #10621381 | 2 |
| C2×#6461 | 3 |
| C2×#898 | 7 |