Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
410 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×#88413 | C2 | semidirect |
| 3. C4×C3⋊(C9⋊C8) | C2 | semidirect |
| 4. C9×C4⋊(C3⋊C8) | C2 | semidirect |
| 5. (C2×D9)⋊(C3⋊C8) | C2 | semidirect |
| 37. C3⋊(C9⋊C8) | D4 | semidirect |
| 67. C3×C4×C9 | M16 | semidirect |
| 78. C4⋊(C3⋊C8) | D9 | semidirect |
| 154. C4×C9 | #208 | semidirect |
| 163. C3×C9 | #436 | semidirect |
| 227. C3×C4 | #3663 | semidirect |
| 236. C9 | #5012 | semidirect |
| 265. C4 | #88413 | semidirect |
| 269. C3 | #10588522 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D36 | 2 |
| C2×#88413 | 2 |
| C4×C3⋊(C9⋊C8) | 2 |
| C9×C4⋊(C3⋊C8) | 2 |
| (C2×D9)⋊(C3⋊C8) | 2 |
| #10590339 | 3 |
| #10588522 | 3 |