Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
284 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 4. #10620489 | C2 | semidirect |
| 5. #10620486 | C2 | semidirect |
| 12. C7×#208 | C4 | semidirect |
| 14. C3×#1136 | C4 | semidirect |
| 30. C3×C7⋊C8 | C2×C4 | semidirect |
| 31. C7×C3⋊C8 | C2×C4 | semidirect |
| 39. #1136 | Dic3 | semidirect |
| 53. Dic21 | M16 | semidirect |
| 64. C7⋊C8 | C2×Dic3 | semidirect |
| 72. #208 | Dic7 | semidirect |
| 99. C3⋊C8 | C2×Dic7 | semidirect |
| 100. C3×C7 | C4×M16 | semidirect |
| 131. C7 | Dic3×M16 | semidirect |
| 143. C3 | M16×Dic7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic21 | 2 |
| C2×C7×#208 | 2 |
| C2×C3×#1136 | 2 |
| #10620489 | 2 |
| #10620486 | 2 |
| M16×Dic7 | 3 |
| Dic3×M16 | 7 |