Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
682 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3672⋊C3 | C2 | semidirect |
| 3. #63486⋊C3 | C2 | semidirect |
| 4. #63392⋊C3 | C2 | semidirect |
| 5. #63389⋊C3 | C2 | semidirect |
| 7. #10588897 | C3 | semidirect |
| 13. C2×3−1+2⋊Q8 | C22 | semidirect |
| 16. C4⋊(3−1+2⋊C4) | C22 | semidirect |
| 18. C2×3−1+2⋊C8 | C22 | semidirect |
| 26. C2×#3672 | C2×C3 | semidirect |
| 27. #63486 | C2×C3 | semidirect |
| 28. #63392 | C2×C3 | semidirect |
| 29. #63389 | C2×C3 | semidirect |
| 68. C2×Dic18 | C22×C3 | semidirect |
| 71. C4⋊Dic9 | C22×C3 | semidirect |
| 73. C2×C9⋊C8 | C22×C3 | semidirect |
| 80. C22×3−1+2 | SD16 | semidirect |
| 191. C22×C9 | C3×SD16 | semidirect |
| 204. 3−1+2 | #450 | semidirect |
| 287. C9 | C3×#450 | semidirect |
| 319. C22 | #3672⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×3−1+2 | 2 |
| C2×#3672⋊C3 | 2 |
| #63486⋊C3 | 2 |
| #63392⋊C3 | 2 |
| #63389⋊C3 | 2 |
| C3×#5218 | 3 |
| #10588897 | 3 |