Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
278 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 278 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. #11720534 | C2 | semidirect |
| 3. C2×C9×C3⋊C16 | C2 | semidirect |
| 4. #11720230 | C2 | semidirect |
| 5. D9×C3⋊C16 | C2 | semidirect |
| 68. C2×C3⋊C16 | D9 | semidirect |
| 130. C3×C9 | #504 | semidirect |
| 181. C9 | #5140 | semidirect |
| 204. C3 | #10588581 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63464 | 2 |
| #11720534 | 2 |
| C2×C9×C3⋊C16 | 2 |
| #11720230 | 2 |
| D9×C3⋊C16 | 2 |
| #10590621 | 3 |
| #10588581 | 3 |