Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
454 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 103 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. C3×#63431 | C2 | semidirect |
| 4. C9×C4⋊(C3⋊C8) | C2 | semidirect |
| 5. #11720276 | C2 | semidirect |
| 26. #63431 | D3 | semidirect |
| 73. C3×C4×C9 | SD16 | semidirect |
| 88. C4⋊(C3⋊C8) | D9 | semidirect |
| 174. C4×C9 | #215 | semidirect |
| 185. C3×C9 | #461 | semidirect |
| 259. C3×C4 | #3664 | semidirect |
| 271. C9 | #5083 | semidirect |
| 303. C4 | #88416 | semidirect |
| 307. C3 | #10588525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C3⋊D9) | 2 |
| C3×#63431 | 2 |
| C2×#88416 | 2 |
| C9×C4⋊(C3⋊C8) | 2 |
| #11720276 | 2 |
| #10590379 | 3 |
| #10588525 | 3 |