Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
220 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 220 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 |
|---|---|---|
| 8. C4⋊Dic21 | C4 | semidirect |
| 11. C4×C7×Dic3 | C4 | semidirect |
| 13. C3×#1136 | C4 | semidirect |
| 38. #1136 | Dic3 | semidirect |
| 74. C4×Dic3 | Dic7 | semidirect |
| 103. C3×C7 | #339 | semidirect |
| 139. C7 | #4555 | semidirect |
| 154. C3 | #89318 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621409 | 2 |
| C2×C4×C7×Dic3 | 2 |
| C2×C3×#1136 | 2 |
| #89318 | 3 |
| #4555 | 7 |