Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3906 conjugacy classes of subgroups; only the 735 normal subgroups are shown.
This group has 3906 conjugacy classes of subgroups — too many to draw. Only its 735 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×Q8×C3⋊D3 | C2 | semidirect |
| 2. Q8×#1113 | C2 | direct (N × H) |
| 4. C2×#89040 | C2 | semidirect |
| 7. C2×C33×Q8 | C22 | semidirect |
| 8. C3×Q8×C3⋊D3 | C22 | semidirect |
| 10. C2×C3×#634 | C22 | semidirect |
| 11. C2×#6296 | C22 | semidirect |
| 14. #89040 | C22 | semidirect |
| 15. C2×Q8×C3⋊D3 | D3 | semidirect |
| 23. C2×#1113 | Q8 | direct (N × H) |
| 25. C33×Q8 | C23 | semidirect |
| 29. C3×#634 | C23 | semidirect |
| 30. #6296 | C23 | semidirect |
| 36. C2×C32×Q8 | C2×D3 | semidirect |
| 37. Q8×C3⋊D3 | C2×D3 | semidirect |
| 39. C2×#634 | C2×D3 | semidirect |
| 53. C2×C3×C3⋊D3 | C2×Q8 | semidirect |
| 55. #1113 | C2×Q8 | direct (N × H) |
| 72. C32×Q8 | C22×D3 | semidirect |
| 78. #634 | C22×D3 | semidirect |
| 89. C2×C33 | C22×Q8 | semidirect |
| 91. C3×C3⋊D3 | C22×Q8 | semidirect |
| 97. C2×C3×Q8 | D32 | semidirect |
| 114. C2×C3⋊D3 | D3×Q8 | semidirect |
| 131. C33 | C23×Q8 | semidirect |
| 140. C3×Q8 | C2×D32 | semidirect |
| 159. C2×C32 | C2×D3×Q8 | semidirect |
| 161. C3⋊D3 | C2×D3×Q8 | semidirect |
| 169. C2×Q8 | #1113 | direct (N × H) |
| 191. C32 | C22×D3×Q8 | semidirect |
| 197. Q8 | C2×#1113 | direct (N × H) |
| 207. C2×C3 | D32×Q8 | semidirect |
| 219. C3 | C2×D32×Q8 | semidirect |
| 221. C2 | Q8×#1113 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×C3⋊D3 | 2 |
| Q8×#1113 | 2 |
| C2×C4×#1113 | 2 |
| C2×#89040 | 2 |
| C2×D32×Q8 | 3 |