Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
284 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 74 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×#66634 | C2 | semidirect |
| 2. C2×C7×#215 | C2 | semidirect |
| 3. C3×#6507 | C2 | semidirect |
| 5. C2×#66566 | C2 | semidirect |
| 6. C2×#66564 | C2 | semidirect |
| 7. C3⋊C8×Dic7 | C2 | semidirect |
| 23. #6507 | D3 | semidirect |
| 45. C3⋊(C7⋊C8) | D4 | semidirect |
| 46. C7×C3⋊C8 | D4 | semidirect |
| 64. C2×#215 | D7 | semidirect |
| 76. C3×Dic7 | SD16 | semidirect |
| 128. Dic7 | #215 | semidirect |
| 145. C3⋊C8 | C22⋊D7 | semidirect |
| 146. C3×C7 | #492 | semidirect |
| 191. C7 | #5085 | semidirect |
| 206. C3 | #89947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66634 | 2 |
| C2×C7×#215 | 2 |
| C3×#6507 | 2 |
| #10621013 | 2 |
| C2×#66566 | 2 |
| C2×#66564 | 2 |
| C3⋊C8×Dic7 | 2 |
| #89947 | 3 |
| #5085 | 7 |