Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
398 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 105 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. C9×#869 | C2 | semidirect |
| 4. C4⋊(C3⋊(C9⋊C8)) | C2 | semidirect |
| 5. #11720297 | C2 | semidirect |
| 70. C3×C4×C9 | SD16 | semidirect |
| 80. #869 | D9 | semidirect |
| 162. C4×C9 | #214 | semidirect |
| 171. C3×C9 | #461 | semidirect |
| 238. C3×C4 | #3675 | semidirect |
| 248. C9 | #5019 | semidirect |
| 279. C4 | #88425 | semidirect |
| 283. C3 | #10588768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D36 | 2 |
| C9×#869 | 2 |
| C2×#88425 | 2 |
| C4⋊(C3⋊(C9⋊C8)) | 2 |
| #11720297 | 2 |
| #10590363 | 3 |
| #10588768 | 3 |