Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
438 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 106 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. C4×3−1+2⋊Q8 | C2 | semidirect |
| 4. #63392⋊C3 | C2 | semidirect |
| 5. C4⋊(3−1+2⋊C8) | C2 | semidirect |
| 7. #10588752 | C3 | semidirect |
| 25. C2×#3672 | C2×C3 | semidirect |
| 26. C4×Dic18 | C2×C3 | semidirect |
| 27. #63392 | C2×C3 | semidirect |
| 28. C4⋊(C9⋊C8) | C2×C3 | semidirect |
| 40. 3−1+2⋊Q8 | D4 | semidirect |
| 73. C4×3−1+2 | SD16 | semidirect |
| 120. Dic18 | C3×D4 | semidirect |
| 170. C4×C9 | C3×SD16 | semidirect |
| 180. 3−1+2 | #460 | semidirect |
| 251. C9 | C3×#460 | semidirect |
| 280. C4 | #3672⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×#127 | 2 |
| C2×#3672⋊C3 | 2 |
| C4×3−1+2⋊Q8 | 2 |
| #63392⋊C3 | 2 |
| C4⋊(3−1+2⋊C8) | 2 |
| C3×#5075 | 3 |
| #10588752 | 3 |