Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
298 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×C9×C3⋊C16 | C2 | semidirect |
| 4. #11720230 | C2 | direct (N × H) |
| 12. C3⋊(C9⋊C16) | C22 | semidirect |
| 13. C9×C3⋊C16 | C22 | semidirect |
| 62. C2×C3⋊C16 | D9 | semidirect |
| 84. C2×C3×C9 | M32 | semidirect |
| 102. C3⋊C16 | C2×D9 | semidirect |
| 122. C3×C9 | C2×M32 | semidirect |
| 147. C2×C9 | #812 | semidirect |
| 174. C9 | C2×#812 | semidirect |
| 186. C2×C3 | #63357 | semidirect |
| 198. C3 | C2×#63357 | semidirect |
| 201. C2 | #11720230 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C8×D9 | 2 |
| C2×C3⋊(C9⋊C16) | 2 |
| C2×C9×C3⋊C16 | 2 |
| #11720230 | 2 |
| C2×#63543 | 3 |
| C2×#63357 | 3 |