Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
513 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 513 conjugacy classes of subgroups — too many to draw. Only its 99 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. C4×C4⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 3. C4×#6180 | C2 | semidirect |
| 4. #11720318 | C2 | semidirect |
| 5. #11720315 | C2 | semidirect |
| 14. #88432 | C4 | direct (N × H) |
| 15. C4×C4⋊(C3⋊D3) | D3 | semidirect |
| 29. C4⋊((C3⋊D3)⋊C3) | C2×C4 | semidirect |
| 32. #6180 | C2×C4 | semidirect |
| 55. C4×H(3,𝔽3) | D8 | semidirect |
| 82. C4⋊(C3⋊D3) | C4×D3 | semidirect |
| 133. C32×C4 | #213 | semidirect |
| 143. H(3,𝔽3) | C4×D8 | semidirect |
| 218. C32 | C4×#213 | semidirect |
| 247. C4 | #88432 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊((C3⋊D3)⋊C3) | 2 |
| C2×#88432 | 2 |
| C4×#6180 | 2 |
| #11720318 | 2 |
| #11720315 | 2 |
| C4×#3714 | 3 |