Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 408 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×C9×#204 | C2 | semidirect |
| 2. C2×C3×C8×D9 | C2 | semidirect |
| 4. #11720944 | C2 | semidirect |
| 5. #11720540 | C2 | semidirect |
| 6. #11720298 | C2 | semidirect |
| 7. #11720295 | C2 | semidirect |
| 33. C2×C8×D9 | D3 | semidirect |
| 52. C3×C8×C9 | D4 | semidirect |
| 91. C2×C3×D9 | SD16 | semidirect |
| 104. C2×#204 | D9 | semidirect |
| 147. C8×C9 | #67 | semidirect |
| 204. C2×D9 | #204 | semidirect |
| 222. C3×C9 | #465 | semidirect |
| 256. C3×C8 | #611 | semidirect |
| 318. C9 | #5114 | semidirect |
| 334. C8 | #6194 | semidirect |
| 362. C3 | #10588851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#204 | 2 |
| C2×C3×C8×D9 | 2 |
| #11721036 | 2 |
| #11720944 | 2 |
| #11720540 | 2 |
| #11720298 | 2 |
| #11720295 | 2 |
| #10590829 | 3 |
| #10588851 | 3 |