Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 268 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. #10621413 | C2 | semidirect |
| 2. C22×C7×C3⋊C8 | C2 | semidirect |
| 3. C3×#6493 | C2 | semidirect |
| 4. C2×#66561 | C2 | semidirect |
| 5. #10620525 | C2 | semidirect |
| 6. #10620503 | C2 | semidirect |
| 7. #10620500 | C2 | semidirect |
| 24. #6493 | D3 | semidirect |
| 46. C7×C3⋊C8 | D4 | semidirect |
| 63. C22×C3⋊C8 | D7 | semidirect |
| 69. C22×C3×C7 | D8 | semidirect |
| 128. C22×C7 | #213 | semidirect |
| 157. C3⋊C8 | C22⋊D7 | semidirect |
| 158. C3×C7 | #466 | semidirect |
| 183. C22×C3 | D56 | semidirect |
| 210. C7 | #5038 | semidirect |
| 225. C22 | #66561 | semidirect |
| 232. C3 | #89887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621413 | 2 |
| C22×C7×C3⋊C8 | 2 |
| C3×#6493 | 2 |
| C2×#66561 | 2 |
| #10620525 | 2 |
| #10620503 | 2 |
| #10620500 | 2 |
| #89887 | 3 |
| #5038 | 7 |