Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 228 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 |
|---|---|---|
| 4. C2×#66569 | C2 | semidirect |
| 5. #10620524 | C2 | semidirect |
| 6. #10620507 | C2 | semidirect |
| 7. #10620505 | C2 | semidirect |
| 67. C22×C3×C7 | Q16 | semidirect |
| 118. C22×C7 | #216 | semidirect |
| 142. C3×C7 | #467 | semidirect |
| 162. C22×C3 | #1144 | semidirect |
| 186. C7 | #5051 | semidirect |
| 193. C22 | #66569 | semidirect |
| 202. C3 | #89823 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊(C7⋊C8) | 2 |
| C7×#924 | 2 |
| C3×#6487 | 2 |
| C2×#66569 | 2 |
| #10620524 | 2 |
| #10620507 | 2 |
| #10620505 | 2 |
| #89823 | 3 |
| #5051 | 7 |