Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
580 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 226 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×Q8×D7 | C2 | semidirect |
| 3. C3×C4×C7×Q8 | C2 | semidirect |
| 4. C3×#6460 | C2 | semidirect |
| 5. C3×#6458 | C2 | semidirect |
| 6. C3×#6438 | C2 | semidirect |
| 7. C3×C4×D28 | C2 | semidirect |
| 8. #90267 | C3 | direct (N × H) |
| 23. C2×#1161 | C2×C3 | semidirect |
| 24. C2×Q8×D7 | C2×C3 | semidirect |
| 25. C4×C7×Q8 | C2×C3 | semidirect |
| 26. #6460 | C2×C3 | semidirect |
| 27. #6458 | C2×C3 | semidirect |
| 28. #6438 | C2×C3 | semidirect |
| 29. C4×D28 | C2×C3 | semidirect |
| 33. C3×C7×Q8 | D4 | semidirect |
| 63. C3×C4×Q8 | D7 | semidirect |
| 71. C2×C3×D7 | #41 | semidirect |
| 80. C7×Q8 | C3×D4 | semidirect |
| 115. C4×Q8 | C3×D7 | semidirect |
| 123. C2×D7 | C3×#41 | semidirect |
| 132. C3×Q8 | D28 | semidirect |
| 142. C3×C7 | #548 | semidirect |
| 177. Q8 | C3×D28 | semidirect |
| 187. C7 | C3×#548 | semidirect |
| 205. C3 | #90267 | 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×Q8×D7 | 2 |
| C3×C4×C7×Q8 | 2 |
| C3×#6460 | 2 |
| C3×#6458 | 2 |
| C3×#6438 | 2 |
| C3×C4×D28 | 2 |
| #90267 | 3 |
| C3×#548 | 7 |