Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 88 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. C7×D4×Dic3 | C2 | semidirect |
| 3. Dic3×D28 | C2 | semidirect |
| 4. #10620671 | C2 | semidirect |
| 5. #10620523 | C2 | semidirect |
| 6. #10620499 | C2 | semidirect |
| 7. Dic3×C7⋊C8 | C2 | semidirect |
| 18. C3×#1141 | C4 | semidirect |
| 32. C3×C7×D4 | C2×C4 | semidirect |
| 40. C3×D28 | C2×C4 | semidirect |
| 43. C3×C7⋊C8 | C2×C4 | semidirect |
| 51. #1141 | Dic3 | direct (N × H) |
| 58. D4×Dic3 | D7 | semidirect |
| 75. C7×Dic3 | D8 | semidirect |
| 80. C7×D4 | C2×Dic3 | semidirect |
| 88. D28 | C2×Dic3 | semidirect |
| 91. C7⋊C8 | C2×Dic3 | semidirect |
| 134. C3×D4 | C4×D7 | semidirect |
| 144. C3×C7 | C4×D8 | semidirect |
| 174. Dic3 | #1141 | direct (N × H) |
| 180. D4 | Dic3×D7 | semidirect |
| 190. C7 | Dic3×D8 | semidirect |
| 209. C3 | C4×#1141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×D4×Dic3 | 2 |
| C2×C3×#1141 | 2 |
| Dic3×D28 | 2 |
| #10620671 | 2 |
| #10620523 | 2 |
| #10620499 | 2 |
| Dic3×C7⋊C8 | 2 |
| C4×#1141 | 3 |
| Dic3×D8 | 7 |