Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
376 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 2. C2×#66633 | C2 | semidirect |
| 3. #10620927 | C2 | semidirect |
| 4. C2×#66567 | C2 | semidirect |
| 5. C3×#6406 | C2 | semidirect |
| 6. #10620501 | C2 | semidirect |
| 7. (C2×D3)⋊(C7⋊C8) | C2 | semidirect |
| 11. C2×Dic42 | C22 | semidirect |
| 18. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 19. C3×C4⋊Dic7 | C22 | semidirect |
| 20. C2×C3×C7⋊C8 | C22 | semidirect |
| 29. #6406 | D3 | semidirect |
| 64. C4⋊Dic7 | C2×D3 | semidirect |
| 67. C2×C7⋊C8 | C2×D3 | semidirect |
| 85. C2×D3×C7 | SD16 | semidirect |
| 178. C3×C7 | #450 | semidirect |
| 210. C2×D3 | #1142 | semidirect |
| 237. C7 | #4776 | semidirect |
| 260. C3 | #89990 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C7×D4 | 2 |
| C2×#66633 | 2 |
| #10620927 | 2 |
| C2×#66567 | 2 |
| C3×#6406 | 2 |
| #10620501 | 2 |
| (C2×D3)⋊(C7⋊C8) | 2 |
| #89990 | 3 |
| #4776 | 7 |