Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
256 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 68 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. Q8×Dic21 | C2 | semidirect |
| 2. C2×C7×#215 | C2 | semidirect |
| 3. C2×C3×#1143 | C2 | semidirect |
| 5. #10620518 | C2 | semidirect |
| 6. #10620502 | C2 | semidirect |
| 7. #10620500 | C2 | semidirect |
| 24. C2×#1143 | D3 | semidirect |
| 33. C3×C7×Q8 | D4 | semidirect |
| 62. C2×#215 | D7 | semidirect |
| 79. Dic21 | SD16 | semidirect |
| 84. C7×Q8 | #67 | semidirect |
| 139. C3×Q8 | C22⋊D7 | semidirect |
| 153. C3×C7 | #460 | semidirect |
| 188. Q8 | #4245 | semidirect |
| 202. C7 | #5163 | semidirect |
| 221. C3 | #89935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic21 | 2 |
| C2×C7×#215 | 2 |
| C2×C3×#1143 | 2 |
| #10621025 | 2 |
| #10620518 | 2 |
| #10620502 | 2 |
| #10620500 | 2 |
| #89935 | 3 |
| #5163 | 7 |