Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
810 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×#88746 | C2 | semidirect |
| 2. C2×C3×C9×SD16 | C2 | semidirect |
| 3. #11721838 | C2 | semidirect |
| 4. C2×#88544 | C2 | semidirect |
| 5. #11720582 | C2 | semidirect |
| 6. #11720543 | C2 | semidirect |
| 7. #11720542 | C2 | semidirect |
| 33. C2×C9×SD16 | D3 | semidirect |
| 43. C3×Q8×C9 | D4 | semidirect |
| 53. C4⋊(C3⋊D9) | D4 | semidirect |
| 108. C2×C3×SD16 | D9 | semidirect |
| 144. Q8×C9 | #67 | semidirect |
| 228. C2×SD16 | C3⋊D9 | semidirect |
| 234. C3×C9 | #449 | semidirect |
| 243. C3×Q8 | #611 | semidirect |
| 333. C9 | #5172 | semidirect |
| 338. Q8 | #6233 | semidirect |
| 381. C3 | #10588852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88746 | 2 |
| C2×C3×C9×SD16 | 2 |
| #11721838 | 2 |
| C2×#88544 | 2 |
| #11720582 | 2 |
| #11720543 | 2 |
| #11720542 | 2 |
| #10592871 | 3 |
| #10588852 | 3 |