Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
624 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 230 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. C3×C4×C7×Q8 | C2 | semidirect |
| 3. C3×#6458 | C2 | semidirect |
| 4. C3×#6437 | C2 | semidirect |
| 5. C3×C4×D28 | C2 | semidirect |
| 6. #90268 | C3 | direct (N × H) |
| 17. C2×#1161 | C2×C3 | semidirect |
| 18. C4×C7×Q8 | C2×C3 | semidirect |
| 19. #6458 | C2×C3 | semidirect |
| 20. #6437 | C2×C3 | semidirect |
| 21. C4×D28 | C2×C3 | semidirect |
| 24. C3×C7×Q8 | D4 | semidirect |
| 46. C3×C4×Q8 | D7 | semidirect |
| 54. C3×C4×C7 | #41 | semidirect |
| 58. C7×Q8 | C3×D4 | semidirect |
| 84. C4×Q8 | C3×D7 | semidirect |
| 92. C4×C7 | C3×#41 | semidirect |
| 95. C3×Q8 | D28 | semidirect |
| 104. C3×C7 | #550 | semidirect |
| 126. C3×C4 | #1161 | semidirect |
| 128. Q8 | C3×D28 | semidirect |
| 137. C7 | C3×#550 | semidirect |
| 149. C4 | C3×#1161 | semidirect |
| 150. C3 | #90268 | 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 |
| C3×C4×C7×Q8 | 2 |
| C3×#6458 | 2 |
| C3×#6437 | 2 |
| C3×C4×D28 | 2 |
| #90268 | 3 |
| C3×#550 | 7 |