Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 75 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. C3×C4×C7×D4 | C2 | semidirect |
| 2. C2×#66633 | C2 | semidirect |
| 4. #10621358 | C2 | semidirect |
| 5. #10620649 | C2 | semidirect |
| 6. #10620648 | C2 | semidirect |
| 7. C4⋊(C3⋊(C7⋊C8)) | C2 | semidirect |
| 22. C4×C7×D4 | D3 | semidirect |
| 59. C3×C4×D4 | D7 | semidirect |
| 117. C4×D4 | D21 | semidirect |
| 150. C3×C7 | #463 | semidirect |
| 198. C7 | #5016 | semidirect |
| 217. C3 | #89788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×D4 | 2 |
| C2×#66633 | 2 |
| C2×#66632 | 2 |
| #10621358 | 2 |
| #10620649 | 2 |
| #10620648 | 2 |
| C4⋊(C3⋊(C7⋊C8)) | 2 |
| #89788 | 3 |
| #5016 | 7 |