Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1512 conjugacy classes of subgroups; only the 515 normal subgroups are shown.
This group has 1512 conjugacy classes of subgroups — too many to draw. Only its 515 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 |
|---|---|---|
| 2. #11723910 | C2 | semidirect |
| 4. #11722177 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊(C3⋊C8))) | C2 | semidirect |
| 23. C33×D4 | Q8 | semidirect |
| 59. C32×D4 | Dic6 | semidirect |
| 97. C33 | #474 | semidirect |
| 100. C3×D4 | #634 | semidirect |
| 132. C32 | #5007 | semidirect |
| 136. D4 | #6308 | semidirect |
| 158. C3 | #10592706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4×D4 | 2 |
| #11723910 | 2 |
| #11722202 | 2 |
| #11722177 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| #10592706 | 3 |