Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×C3×#1161 | C2 | semidirect |
| 2. C2×C3×#1143 | C2 | semidirect |
| 3. C2×C3×D56 | C2 | semidirect |
| 4. C3×#6458 | C2 | semidirect |
| 5. C3×C7×#103 | C2 | semidirect |
| 6. C3×(C2×D7)⋊C8 | C2 | semidirect |
| 7. C3×#6383 | C2 | semidirect |
| 8. #89583 | C3 | direct (N × H) |
| 24. C2×#1161 | C2×C3 | semidirect |
| 25. C2×#1143 | C2×C3 | semidirect |
| 26. C2×D56 | C2×C3 | semidirect |
| 27. #6458 | C2×C3 | semidirect |
| 28. C7×#103 | C2×C3 | semidirect |
| 29. (C2×D7)⋊C8 | C2×C3 | semidirect |
| 30. #6383 | C2×C3 | semidirect |
| 36. C3×C7×Q8 | D4 | semidirect |
| 46. C3×D28 | D4 | semidirect |
| 71. C3×#103 | D7 | semidirect |
| 94. C7×Q8 | C3×D4 | semidirect |
| 104. D28 | C3×D4 | semidirect |
| 135. #103 | C3×D7 | semidirect |
| 157. C3×Q8 | D28 | semidirect |
| 173. C3×C7 | #449 | semidirect |
| 214. Q8 | C3×D28 | semidirect |
| 230. C7 | C3×#449 | semidirect |
| 252. C3 | #89583 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1161 | 2 |
| C2×C3×#1143 | 2 |
| C2×C3×D56 | 2 |
| C3×#6458 | 2 |
| C3×C7×#103 | 2 |
| C3×(C2×D7)⋊C8 | 2 |
| C3×#6383 | 2 |
| #89583 | 3 |
| C3×#449 | 7 |