Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
280 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 280 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×#66632 | C2 | semidirect |
| 2. C2×C7×#213 | C2 | semidirect |
| 3. C3×D4×Dic7 | C2 | semidirect |
| 4. #10621013 | C2 | semidirect |
| 5. Dic7⋊(C3⋊C8) | C2 | semidirect |
| 6. #10620503 | C2 | semidirect |
| 7. #10620501 | C2 | semidirect |
| 24. D4×Dic7 | D3 | semidirect |
| 34. C3×C7×D4 | D4 | semidirect |
| 63. C2×#213 | D7 | semidirect |
| 82. C3×Dic7 | D8 | semidirect |
| 90. C7×D4 | D12 | semidirect |
| 142. Dic7 | #213 | semidirect |
| 147. C3×D4 | C22⋊D7 | semidirect |
| 161. C3×C7 | #459 | semidirect |
| 206. D4 | #4247 | semidirect |
| 214. C7 | #5015 | semidirect |
| 236. C3 | #89922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66632 | 2 |
| C2×C7×#213 | 2 |
| C3×D4×Dic7 | 2 |
| #10621013 | 2 |
| Dic7⋊(C3⋊C8) | 2 |
| #10620503 | 2 |
| #10620501 | 2 |
| #89922 | 3 |
| #5015 | 7 |