Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
256 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 72 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×#66634 | C2 | semidirect |
| 2. C7×Q8×Dic3 | C2 | semidirect |
| 3. C2×C3×#1143 | C2 | semidirect |
| 5. Dic3⋊(C7⋊C8) | C2 | semidirect |
| 6. #10620504 | C2 | semidirect |
| 7. #10620499 | C2 | semidirect |
| 24. C2×#1143 | D3 | semidirect |
| 33. C3×C7×Q8 | D4 | semidirect |
| 61. Q8×Dic3 | D7 | semidirect |
| 79. C7×Dic3 | SD16 | semidirect |
| 84. C7×Q8 | #67 | semidirect |
| 139. C3×Q8 | D28 | semidirect |
| 153. C3×C7 | #460 | semidirect |
| 184. Dic3 | #1143 | semidirect |
| 188. Q8 | #4246 | semidirect |
| 202. C7 | #5163 | semidirect |
| 221. C3 | #89799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66634 | 2 |
| C7×Q8×Dic3 | 2 |
| C2×C3×#1143 | 2 |
| #10621020 | 2 |
| Dic3⋊(C7⋊C8) | 2 |
| #10620504 | 2 |
| #10620499 | 2 |
| #89799 | 3 |
| #5163 | 7 |