Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
790 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 790 conjugacy classes of subgroups — too many to draw. Only its 211 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. C22×C3×Q8×C9 | C2 | semidirect |
| 2. C2×#88548 | C2 | semidirect |
| 4. #11720582 | C2 | semidirect |
| 5. #11720571 | C2 | semidirect |
| 22. C22×Q8×C9 | D3 | semidirect |
| 33. C3×Q8×C9 | D4 | semidirect |
| 69. C22×C3×C9 | SD16 | semidirect |
| 78. C22×C3×Q8 | D9 | semidirect |
| 106. Q8×C9 | #67 | semidirect |
| 157. C22×C9 | #215 | semidirect |
| 166. C22×Q8 | C3⋊D9 | semidirect |
| 171. C3×C9 | #448 | semidirect |
| 180. C3×Q8 | #611 | semidirect |
| 225. C22×C3 | #3675 | semidirect |
| 244. C9 | #5227 | semidirect |
| 249. Q8 | #6233 | semidirect |
| 274. C22 | #88548 | semidirect |
| 280. C3 | #10588908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Q8×C9 | 2 |
| C2×#88548 | 2 |
| #11721819 | 2 |
| #11720582 | 2 |
| #11720571 | 2 |
| #10592926 | 3 |
| #10588908 | 3 |