Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 240 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. C7×Q8×Dic3 | C2 | semidirect |
| 4. C3×#6409 | C2 | semidirect |
| 5. #10620524 | C2 | semidirect |
| 7. #10620488 | C2 | semidirect |
| 12. #66634 | C4 | semidirect |
| 24. #6409 | D3 | semidirect |
| 31. C3×C7×Q8 | C2×C4 | semidirect |
| 41. C3⋊(C7⋊C8) | C2×C4 | semidirect |
| 55. Q8×Dic3 | D7 | semidirect |
| 76. C7×Q8 | C4×D3 | semidirect |
| 124. C3×Q8 | C4×D7 | semidirect |
| 136. C3×C7 | #440 | semidirect |
| 166. Q8 | D21⋊C4 | semidirect |
| 178. C7 | #4817 | semidirect |
| 194. C3 | #89798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66634 | 2 |
| C7×Q8×Dic3 | 2 |
| #10620990 | 2 |
| C3×#6409 | 2 |
| #10620524 | 2 |
| #10620504 | 2 |
| #10620488 | 2 |
| #89798 | 3 |
| #4817 | 7 |