Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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×C3×#3699 | C2 | semidirect |
| 2. C2×C9×#213 | C2 | semidirect |
| 3. #11721036 | C2 | semidirect |
| 4. C2×#88423 | C2 | semidirect |
| 5. #11720576 | C2 | semidirect |
| 6. (C2×D9)⋊(C3⋊C8) | C2 | semidirect |
| 7. #11720276 | C2 | semidirect |
| 29. C2×#3699 | D3 | semidirect |
| 44. C3×D4×C9 | D4 | semidirect |
| 56. C3×Dic18 | D4 | semidirect |
| 116. C2×#213 | D9 | semidirect |
| 154. D4×C9 | #67 | semidirect |
| 167. Dic18 | #67 | semidirect |
| 255. C3×C9 | #449 | semidirect |
| 272. C3×D4 | #611 | semidirect |
| 372. C9 | #5238 | semidirect |
| 383. D4 | #6194 | semidirect |
| 425. C3 | #10588838 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3699 | 2 |
| C2×C9×#213 | 2 |
| #11721036 | 2 |
| C2×#88423 | 2 |
| #11720576 | 2 |
| (C2×D9)⋊(C3⋊C8) | 2 |
| #11720276 | 2 |
| #10591450 | 3 |
| #10588838 | 3 |