Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 70 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×D7×Dic6 | C2 | semidirect |
| 3. C2×#66565 | C2 | semidirect |
| 4. C2×#66563 | C2 | semidirect |
| 5. #10620649 | C2 | semidirect |
| 6. C7×#810 | C2 | semidirect |
| 7. (C2×D7)⋊(C3⋊C8) | C2 | semidirect |
| 38. Dic42 | D4 | semidirect |
| 41. C7×Dic6 | D4 | semidirect |
| 73. #810 | D7 | semidirect |
| 80. C2×C3×D7 | SD16 | semidirect |
| 141. C2×D7 | #214 | semidirect |
| 165. Dic6 | D28 | semidirect |
| 168. C3×C7 | #448 | semidirect |
| 222. C7 | #5040 | semidirect |
| 241. C3 | #89578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×Dic6 | 2 |
| C3×#6458 | 2 |
| C2×#66565 | 2 |
| C2×#66563 | 2 |
| #10620649 | 2 |
| C7×#810 | 2 |
| (C2×D7)⋊(C3⋊C8) | 2 |
| #89578 | 3 |
| #5040 | 7 |