Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 76 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. C22×Dic42 | C2 | semidirect |
| 3. C2×#66565 | C2 | semidirect |
| 4. C7×#830 | C2 | semidirect |
| 5. #10620509 | C2 | semidirect |
| 33. Dic42 | D4 | semidirect |
| 52. #830 | D7 | semidirect |
| 56. C22×C3×C7 | SD16 | semidirect |
| 103. C22×C7 | #214 | semidirect |
| 126. C3×C7 | #448 | semidirect |
| 148. C22×C3 | #1132 | semidirect |
| 168. C7 | #5040 | semidirect |
| 179. C22 | #66565 | semidirect |
| 185. C3 | #89510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic42 | 2 |
| C3×#6493 | 2 |
| C2×#66565 | 2 |
| C7×#830 | 2 |
| #10620509 | 2 |
| #89510 | 3 |
| #5040 | 7 |