Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 80 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×C7×Dic6 | C2 | semidirect |
| 3. C2×#66568 | C2 | semidirect |
| 4. C3×C22⋊(C7⋊C8) | C2 | semidirect |
| 5. #10620508 | C2 | semidirect |
| 22. C22⋊(C7⋊C8) | D3 | semidirect |
| 36. C7×Dic6 | D4 | semidirect |
| 49. C22×Dic6 | D7 | semidirect |
| 56. C22×C3×C7 | SD16 | semidirect |
| 103. C22×C7 | #204 | semidirect |
| 124. Dic6 | C22⋊D7 | semidirect |
| 126. C3×C7 | #448 | semidirect |
| 145. C22×C3 | #1143 | semidirect |
| 168. C7 | #4738 | semidirect |
| 179. C22 | #66568 | semidirect |
| 185. C3 | #89999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Dic6 | 2 |
| #10621413 | 2 |
| C2×#66568 | 2 |
| C3×C22⋊(C7⋊C8) | 2 |
| #10620508 | 2 |
| #89999 | 3 |
| #4738 | 7 |