Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3108 conjugacy classes of subgroups; only the 895 normal subgroups are shown.
This group has 3108 conjugacy classes of subgroups — too many to draw. Only its 895 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 |
|---|---|---|
| 4. #11723931 | C2 | semidirect |
| 5. #11723929 | C2 | semidirect |
| 7. C4×#6308 | C2 | semidirect |
| 32. C2×C33×C4 | Q8 | semidirect |
| 74. C2×C32×C4 | Dic6 | semidirect |
| 118. C33 | #533 | semidirect |
| 120. C2×C3×C4 | #634 | semidirect |
| 156. C32 | #5517 | semidirect |
| 163. C2×C4 | #6308 | semidirect |
| 179. C3 | #10595988 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#117 | 2 |
| #11723967 | 2 |
| C2×C4×C3⋊(C3⋊Dic3) | 2 |
| #11723931 | 2 |
| #11723929 | 2 |
| #11723919 | 2 |
| C4×#6308 | 2 |
| #10595988 | 3 |