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. C7×D4×Dic3 | C2 | semidirect |
| 3. C2×C3×#1141 | C2 | semidirect |
| 4. #10621020 | C2 | semidirect |
| 5. Dic3⋊(C7⋊C8) | C2 | semidirect |
| 6. #10620504 | C2 | semidirect |
| 7. #10620499 | C2 | semidirect |
| 24. C2×#1141 | D3 | semidirect |
| 34. C3×C7×D4 | D4 | semidirect |
| 63. D4×Dic3 | D7 | semidirect |
| 82. C7×Dic3 | D8 | semidirect |
| 88. C7×D4 | #67 | semidirect |
| 149. C3×D4 | D28 | semidirect |
| 161. C3×C7 | #459 | semidirect |
| 195. Dic3 | #1141 | semidirect |
| 206. D4 | #4246 | semidirect |
| 214. C7 | #5150 | semidirect |
| 236. C3 | #89787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66632 | 2 |
| C7×D4×Dic3 | 2 |
| C2×C3×#1141 | 2 |
| #10621020 | 2 |
| Dic3⋊(C7⋊C8) | 2 |
| #10620504 | 2 |
| #10620499 | 2 |
| #89787 | 3 |
| #5150 | 7 |