Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
980 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 980 conjugacy classes of subgroups — too many to draw. Only its 238 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 |
| 3. C3×#63636 | C2 | semidirect |
| 4. C3×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 5. #10592787 | C3 | direct (N × H) |
| 16. C32×C4⋊Q8 | D3 | semidirect |
| 17. C32×C4⋊Q8 | C2×C3 | semidirect |
| 20. #63636 | C2×C3 | semidirect |
| 21. C4×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 65. C3×C4⋊Q8 | C3×D3 | semidirect |
| 66. C3×C4⋊Q8 | C3⋊D3 | semidirect |
| 144. C4⋊Q8 | C3×C3⋊D3 | semidirect |
| 148. C33 | #486 | semidirect |
| 215. C32 | #5088 | semidirect |
| 216. C32 | C3×#486 | semidirect |
| 247. C3 | C3×#5088 | semidirect |
| 248. C3 | #10592787 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4⋊Q8 | 2 |
| C3×#64083 | 2 |
| C3×#63636 | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| #10592787 | 3 |
| C3×#5088 | 3 |