Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
762 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 182 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 |
| 3. C3×C9⋊#95 | C2 | semidirect |
| 5. #10588911 | C3 | direct (N × H) |
| 14. C22×Q8×C9 | C2×C3 | semidirect |
| 17. C9⋊#95 | C2×C3 | semidirect |
| 21. C22×C3×D9 | Q8 | semidirect |
| 50. C22×C3×Q8 | D9 | semidirect |
| 69. C22×D9 | C3×Q8 | semidirect |
| 115. C22×Q8 | C3×D9 | semidirect |
| 118. C3×C9 | #393 | semidirect |
| 179. C9 | C3×#393 | semidirect |
| 209. C3 | #10588911 | direct (N × H) |
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×C3×(C2×D9)⋊C4 | 2 |
| C3×C9⋊#95 | 2 |
| C3×#5231 | 3 |
| #10588911 | 3 |