Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
420 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 74 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. #10621123 | C2 | semidirect |
| 3. C7×#834 | C2 | semidirect |
| 4. C3×#6408 | C2 | semidirect |
| 5. #10620532 | C2 | semidirect |
| 7. C23×D21 | C4 | semidirect |
| 10. C2×#4268 | C4 | semidirect |
| 14. C2×D84 | C4 | semidirect |
| 15. C2×C4×D21 | C4 | semidirect |
| 17. C7×#217 | C22 | semidirect |
| 18. C3×C22⋊Dic7 | C22 | semidirect |
| 23. #6408 | D3 | semidirect |
| 26. C23×C3×C7 | C2×C4 | semidirect |
| 34. C22×D21 | C2×C4 | semidirect |
| 38. C2×C3×C4×C7 | C2×C4 | semidirect |
| 41. C2×Dic21 | C2×C4 | semidirect |
| 59. C22⋊Dic7 | C2×D3 | semidirect |
| 64. #834 | D7 | semidirect |
| 87. C23×C7 | C4×D3 | semidirect |
| 100. C2×C4×C7 | C4×D3 | semidirect |
| 120. #217 | C2×D7 | semidirect |
| 129. D21 | #99 | semidirect |
| 155. C23×C3 | C4×D7 | semidirect |
| 168. C2×C3×C4 | C4×D7 | semidirect |
| 177. C3×C7 | C2×#99 | semidirect |
| 228. C23 | D21⋊C4 | semidirect |
| 240. C2×C4 | D21⋊C4 | semidirect |
| 241. C7 | D3×#99 | semidirect |
| 270. C3 | D7×#99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D21 | 2 |
| #10621123 | 2 |
| C7×#834 | 2 |
| C3×#6408 | 2 |
| #10620532 | 2 |
| D7×#99 | 3 |
| D3×#99 | 7 |