Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
244 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 80 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. C3×Q8×Dic7 | C2 | semidirect |
| 4. C7×#835 | C2 | semidirect |
| 5. #10620521 | C2 | semidirect |
| 7. C3⋊C8×Dic7 | C2 | semidirect |
| 12. #66634 | C4 | semidirect |
| 21. Q8×Dic7 | D3 | semidirect |
| 31. C3×C7×Q8 | C2×C4 | semidirect |
| 41. C3⋊(C7⋊C8) | C2×C4 | semidirect |
| 58. #835 | D7 | semidirect |
| 71. C3×Dic7 | SD16 | semidirect |
| 76. C7×Q8 | C4×D3 | semidirect |
| 121. Dic7 | #215 | semidirect |
| 124. C3×Q8 | C4×D7 | semidirect |
| 136. C3×C7 | C4×SD16 | semidirect |
| 166. Q8 | D21⋊C4 | semidirect |
| 178. C7 | C4×#215 | semidirect |
| 194. C3 | #89560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66634 | 2 |
| C3×Q8×Dic7 | 2 |
| #10620980 | 2 |
| C7×#835 | 2 |
| #10620521 | 2 |
| #10620503 | 2 |
| C3⋊C8×Dic7 | 2 |
| #89560 | 3 |
| C4×#215 | 7 |