Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 88 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×C7×#208 | C2 | semidirect |
| 3. C2×D7×C3⋊C8 | C2 | semidirect |
| 4. #10620669 | C2 | semidirect |
| 5. Dic7⋊(C3⋊C8) | C2 | semidirect |
| 6. (C2×D7)⋊(C3⋊C8) | C2 | semidirect |
| 7. #10620487 | C2 | semidirect |
| 45. C7×C3⋊C8 | D4 | semidirect |
| 60. C2×#208 | D7 | semidirect |
| 72. C2×C3×D7 | M16 | semidirect |
| 127. C2×D7 | #208 | semidirect |
| 149. C3⋊C8 | C22⋊D7 | semidirect |
| 150. C3×C7 | #435 | semidirect |
| 198. C7 | #5011 | semidirect |
| 217. C3 | #89899 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#208 | 2 |
| C3×C4×C22⋊D7 | 2 |
| C2×D7×C3⋊C8 | 2 |
| #10620669 | 2 |
| Dic7⋊(C3⋊C8) | 2 |
| (C2×D7)⋊(C3⋊C8) | 2 |
| #10620487 | 2 |
| #89899 | 3 |
| #5011 | 7 |