Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1708 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1708 conjugacy classes of subgroups — too many to draw. Only its 469 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×#88850 | C2 | semidirect |
| 3. C33×C4⋊C8 | C2 | semidirect |
| 4. #11722190 | C2 | semidirect |
| 5. C4×C3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 18. C32×C4⋊C8 | D3 | semidirect |
| 31. C3⋊(C3⋊(C3⋊C8)) | D4 | semidirect |
| 47. C33×C4 | M16 | semidirect |
| 53. C3×C4⋊C8 | C3⋊D3 | semidirect |
| 86. C32×C4 | ΓL(1,𝔽25) | semidirect |
| 92. C4⋊C8 | C3⋊(C3⋊D3) | semidirect |
| 95. C33 | #436 | semidirect |
| 125. C3×C4 | #3743 | semidirect |
| 129. C32 | #4838 | semidirect |
| 151. C4 | #88850 | semidirect |
| 154. C3 | #10592537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88850 | 2 |
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C33×C4⋊C8 | 2 |
| #11722190 | 2 |
| C4×C3⋊(C3⋊(C3⋊C8)) | 2 |
| #10592537 | 3 |