Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
280 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 109 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×C3⋊(C9⋊C16) | C2 | semidirect |
| 3. C9×#812 | C2 | semidirect |
| 4. #11720230 | C2 | semidirect |
| 5. D9×C3⋊C16 | C2 | semidirect |
| 65. #812 | D9 | semidirect |
| 132. C3×C9 | #504 | semidirect |
| 183. C9 | #5140 | semidirect |
| 206. C3 | #10588587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63464 | 2 |
| C2×C3⋊(C9⋊C16) | 2 |
| C9×#812 | 2 |
| #11720230 | 2 |
| D9×C3⋊C16 | 2 |
| #10590622 | 3 |
| #10588587 | 3 |