Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
340 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 2. C2×C4×Dic21 | C2 | semidirect |
| 3. C2×C7×#208 | C2 | semidirect |
| 4. #10620511 | C2 | direct (N × H) |
| 11. C3×#1157 | C4 | semidirect |
| 13. C2×C3×D28 | C4 | semidirect |
| 15. C2×C3×Dic14 | C4 | semidirect |
| 17. C4×Dic21 | C22 | semidirect |
| 19. C7×#208 | C22 | semidirect |
| 40. C3×D28 | C2×C4 | semidirect |
| 44. C3×Dic14 | C2×C4 | semidirect |
| 51. #1157 | Dic3 | semidirect |
| 53. C2×D28 | Dic3 | semidirect |
| 55. C2×Dic14 | Dic3 | semidirect |
| 63. C2×#208 | D7 | semidirect |
| 92. D28 | C2×Dic3 | semidirect |
| 96. Dic14 | C2×Dic3 | semidirect |
| 111. #208 | C2×D7 | semidirect |
| 115. C2×C3×C7 | #104 | semidirect |
| 154. C3×C7 | C2×#104 | semidirect |
| 172. C2×C7 | #837 | semidirect |
| 207. C7 | C2×#837 | semidirect |
| 211. C2×C3 | #6399 | semidirect |
| 225. C3 | C2×#6399 | semidirect |
| 229. C2 | #10620511 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1157 | 2 |
| C2×C4×Dic21 | 2 |
| C2×C7×#208 | 2 |
| #10620511 | 2 |
| C2×#6399 | 3 |
| C2×#837 | 7 |