Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
280 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 68 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×#940 | C2 | semidirect |
| 2. C2×C3×#1141 | C2 | semidirect |
| 3. Dic3×D28 | C2 | semidirect |
| 4. C2×#66560 | C2 | semidirect |
| 5. #10620671 | C2 | semidirect |
| 6. Dic3⋊(C7⋊C8) | C2 | semidirect |
| 7. #10620502 | C2 | semidirect |
| 24. C2×#1141 | D3 | semidirect |
| 44. C3×D28 | D4 | semidirect |
| 62. #940 | D7 | semidirect |
| 82. C7×Dic3 | D8 | semidirect |
| 98. D28 | #67 | semidirect |
| 161. C3×C7 | #459 | semidirect |
| 195. Dic3 | #1141 | semidirect |
| 214. C7 | #5150 | semidirect |
| 236. C3 | #89844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#940 | 2 |
| C2×C3×#1141 | 2 |
| Dic3×D28 | 2 |
| C2×#66560 | 2 |
| #10620671 | 2 |
| Dic3⋊(C7⋊C8) | 2 |
| #10620502 | 2 |
| #89844 | 3 |
| #5150 | 7 |