Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3192 conjugacy classes of subgroups; only the 731 normal subgroups are shown.
This group has 3192 conjugacy classes of subgroups — too many to draw. Only its 731 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. C33×C4×Q8 | C2 | semidirect |
| 2. #11723987 | C2 | semidirect |
| 3. #11723937 | C2 | semidirect |
| 4. C4⋊C4×C3⋊(C3⋊D3) | C2 | semidirect |
| 7. #11723911 | C2 | semidirect |
| 8. #11723910 | C2 | semidirect |
| 26. C32×C4×Q8 | D3 | semidirect |
| 43. C4⋊(C3⋊(C3⋊D3)) | Q8 | semidirect |
| 75. C3×C4×Q8 | C3⋊D3 | semidirect |
| 132. C4×Q8 | C3⋊(C3⋊D3) | semidirect |
| 136. C33 | #554 | semidirect |
| 181. C32 | #5579 | semidirect |
| 210. C3 | #10596050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4×Q8 | 2 |
| #11723987 | 2 |
| #11723937 | 2 |
| C4⋊C4×C3⋊(C3⋊D3) | 2 |
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| #11723911 | 2 |
| #11723910 | 2 |
| #10596050 | 3 |