Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
432 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 111 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. Dic3×D36 | C2 | semidirect |
| 3. #11720540 | C2 | semidirect |
| 4. C9×#815 | C2 | semidirect |
| 5. #11720283 | C2 | semidirect |
| 14. C3×D72 | C4 | semidirect |
| 32. C3×D36 | C2×C4 | semidirect |
| 34. C3×C8×C9 | C2×C4 | semidirect |
| 55. D72 | Dic3 | semidirect |
| 74. #815 | D9 | semidirect |
| 91. D36 | C2×Dic3 | semidirect |
| 95. C8×C9 | C2×Dic3 | semidirect |
| 143. C3×C9 | #442 | semidirect |
| 162. C3×C8 | C4×D9 | semidirect |
| 203. C9 | #5152 | semidirect |
| 212. C8 | Dic3×D9 | semidirect |
| 230. C3 | #10588392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D72 | 2 |
| Dic3×D36 | 2 |
| #11720540 | 2 |
| C9×#815 | 2 |
| #11720283 | 2 |
| #10590771 | 3 |
| #10588392 | 3 |