Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
536 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 89 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×#88634 | C2 | semidirect |
| 2. C2×C3×D72 | C2 | semidirect |
| 3. #11721007 | C2 | semidirect |
| 4. C2×#88425 | C2 | semidirect |
| 5. #11720542 | C2 | semidirect |
| 6. C9×#816 | C2 | semidirect |
| 7. #11720266 | C2 | semidirect |
| 34. C2×D72 | D3 | semidirect |
| 52. C3×D36 | D4 | semidirect |
| 54. C9×Dic6 | D4 | semidirect |
| 123. #816 | D9 | semidirect |
| 162. D36 | #67 | semidirect |
| 256. C3×C9 | #449 | semidirect |
| 297. Dic6 | D36 | semidirect |
| 374. C9 | #5158 | semidirect |
| 427. C3 | #10588490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88634 | 2 |
| C2×C3×D72 | 2 |
| #11721007 | 2 |
| C2×#88425 | 2 |
| #11720542 | 2 |
| C9×#816 | 2 |
| #11720266 | 2 |
| #10590963 | 3 |
| #10588490 | 3 |