Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
520 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 141 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. #11721865 | C2 | semidirect |
| 3. #11721782 | C2 | semidirect |
| 4. C3×C9×#104 | C2 | semidirect |
| 5. #11720555 | C2 | semidirect |
| 6. #11720518 | C2 | semidirect |
| 7. #11720516 | C2 | semidirect |
| 14. #88548 | C4 | semidirect |
| 15. #88547 | C4 | semidirect |
| 16. #88544 | C4 | semidirect |
| 17. #88543 | C4 | semidirect |
| 35. C9×#104 | D3 | semidirect |
| 101. C3×#104 | D9 | semidirect |
| 197. #104 | C3⋊D9 | semidirect |
| 199. C3×C9 | #444 | semidirect |
| 272. C9 | #4823 | semidirect |
| 305. C3 | #10588503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721868 | 2 |
| #11721865 | 2 |
| #11721782 | 2 |
| C3×C9×#104 | 2 |
| #11720555 | 2 |
| #11720518 | 2 |
| #11720516 | 2 |
| #10592522 | 3 |
| #10588503 | 3 |