Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1838 conjugacy classes of subgroups; only the 646 normal subgroups are shown.
This group has 1838 conjugacy classes of subgroups — too many to draw. Only its 646 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. C32×Q8×A4 | C2 | direct (N × H) |
| 3. C23×C32×Q8 | C3 | semidirect |
| 4. C2×C3×Q8×A4 | C3 | direct (N × H) |
| 11. C22×C32×Q8 | C2×C3 | semidirect |
| 13. C3×Q8×A4 | C2×C3 | direct (N × H) |
| 15. C2×C32×A4 | Q8 | direct (N × H) |
| 19. C23×C3×Q8 | C32 | semidirect |
| 20. C2×Q8×A4 | C32 | direct (N × H) |
| 30. C2×C32×Q8 | A4 | direct (N × H) |
| 37. C32×A4 | C2×Q8 | direct (N × H) |
| 42. C22×C3×Q8 | C2×C32 | semidirect |
| 44. Q8×A4 | C2×C32 | direct (N × H) |
| 49. C23×C32 | C3×Q8 | semidirect |
| 51. C2×C3×A4 | C3×Q8 | direct (N × H) |
| 56. C32×Q8 | C2×A4 | direct (N × H) |
| 64. C23×Q8 | C33 | semidirect |
| 76. C2×C3×Q8 | C3×A4 | direct (N × H) |
| 90. C22×C32 | C2×C3×Q8 | semidirect |
| 92. C3×A4 | C2×C3×Q8 | direct (N × H) |
| 99. C22×Q8 | C2×C33 | semidirect |
| 105. C23×C3 | C32×Q8 | semidirect |
| 107. C2×A4 | C32×Q8 | direct (N × H) |
| 112. C3×Q8 | C2×C3×A4 | direct (N × H) |
| 125. C2×C32 | Q8×A4 | direct (N × H) |
| 134. C2×Q8 | C32×A4 | direct (N × H) |
| 147. C22×C3 | C2×C32×Q8 | semidirect |
| 149. A4 | C2×C32×Q8 | direct (N × H) |
| 154. C32 | C2×Q8×A4 | direct (N × H) |
| 158. C23 | C33×Q8 | semidirect |
| 162. Q8 | C2×C32×A4 | direct (N × H) |
| 174. C2×C3 | C3×Q8×A4 | direct (N × H) |
| 183. C22 | C2×C33×Q8 | semidirect |
| 188. C3 | C2×C3×Q8×A4 | direct (N × H) |
| 192. C2 | C32×Q8×A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×Q8×A4 | 2 |
| C2×C32×C4×A4 | 2 |
| C23×C32×Q8 | 3 |
| C2×C3×Q8×A4 | 3 |
| C2×C33×Q8 | 4 |