Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
560 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 160 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×D7×Dic6 | C2 | semidirect |
| 2. C4×Dic42 | C2 | semidirect |
| 3. C7×#869 | C2 | semidirect |
| 5. #10621032 | C2 | semidirect |
| 7. #10620992 | C2 | semidirect |
| 8. #10620921 | C2 | semidirect |
| 42. Dic42 | D4 | semidirect |
| 46. C3×D28 | Q8 | semidirect |
| 73. #869 | D7 | semidirect |
| 78. C2×C3×D7 | C2×Q8 | semidirect |
| 81. C3×C4×C7 | C2×Q8 | semidirect |
| 96. D28 | Dic6 | semidirect |
| 133. C2×D7 | C2×Dic6 | semidirect |
| 136. C4×C7 | C2×Dic6 | semidirect |
| 155. C3×C7 | D4×Q8 | semidirect |
| 184. C3×C4 | Q8×D7 | semidirect |
| 202. C7 | D4×Dic6 | semidirect |
| 216. C4 | D7×Dic6 | semidirect |
| 218. C3 | #90418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×Dic6 | 2 |
| C4×Dic42 | 2 |
| C7×#869 | 2 |
| C3×C4×D28 | 2 |
| #10621032 | 2 |
| #10620996 | 2 |
| #10620992 | 2 |
| #10620921 | 2 |
| #90418 | 3 |
| D4×Dic6 | 7 |