Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
446 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 89 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. #11721715 | C2 | semidirect |
| 3. C4⋊((C3⋊(C3⋊C8))⋊C3) | C2 | semidirect |
| 5. #11720307 | C2 | semidirect |
| 22. C4⋊(C3⋊(C3⋊C8)) | D3 | semidirect |
| 36. C4⋊((C3⋊D3)⋊C3) | Q8 | semidirect |
| 103. C4⋊(C3⋊D3) | Dic6 | semidirect |
| 184. H(3,𝔽3) | #476 | semidirect |
| 280. C32 | #4842 | semidirect |
| 281. C32 | #5008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721715 | 2 |
| C4×C4⋊((C3⋊D3)⋊C3) | 2 |
| C4⋊((C3⋊(C3⋊C8))⋊C3) | 2 |
| #11720308 | 2 |
| #11720307 | 2 |
| #10590300 | 3 |
| #10590266 | 3 |