Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1836 conjugacy classes of subgroups; only the 390 normal subgroups are shown.
This group has 1836 conjugacy classes of subgroups — too many to draw. Only its 390 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. C22×C33×Q8 | C2 | semidirect |
| 3. C32×C3⋊#95 | C2 | semidirect |
| 5. C3×#5231 | C3 | direct (N × H) |
| 12. C22×C32×Q8 | D3 | semidirect |
| 13. C22×C32×Q8 | C2×C3 | semidirect |
| 17. C3×C3⋊#95 | C2×C3 | semidirect |
| 21. C22×C32×D3 | Q8 | semidirect |
| 28. #5231 | C32 | direct (N × H) |
| 50. C22×C3×Q8 | C3×D3 | semidirect |
| 51. C22×C3×Q8 | C2×C32 | semidirect |
| 55. C3⋊#95 | C2×C32 | semidirect |
| 64. C22×C3×D3 | C3×Q8 | semidirect |
| 115. C22×Q8 | C32×D3 | semidirect |
| 118. C33 | #393 | semidirect |
| 127. C22×D3 | C32×Q8 | semidirect |
| 178. C32 | #5231 | direct (N × H) |
| 179. C32 | C3×#393 | semidirect |
| 209. C3 | C3×#5231 | direct (N × H) |
| 210. C3 | C32×#393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×Q8 | 2 |
| C2×C32×(C2×D3)⋊C4 | 2 |
| C32×C3⋊#95 | 2 |
| C32×#393 | 3 |
| C3×#5231 | 3 |